MD, I empathize with you entirely, as I also am 32 and I am interested in romancing a highly intelligent and very attractive girl of 22 - if, that is, she develops a more mature attitude to l'amour and marriage. I know a guy who is something like 13 years older than his babelicious wife, whom he married when she was 21; she's 29 now, but they both appear to be very happy, although he works very hard in the gym - no doubt for her sake. I suppose it all depends on the maturity of the 22 year old, which is not a quality necessarily proportional to intelligence, you must understand.
I don't think you should gratuitously descend to the level of a 22 year old to steal her heart; rather, you must seek to stimulate in her mind admiration for your level of maturity and understanding, so much so that she will even aspire to be mature like you. The clear goal always has to be to see her believe in you. Once a woman believes in a man, it becomes easy for him to win her. I think it is easier for a woman to believe in a man who is older than her if he can demonstrate superior manliness (defined well elsewhere on this site) to that of boys her age. It can therefore work to your advantage being older and wiser, BUT, I doubt if being openly soft and caring and gushing, stereotypes of male maturity, will do the trick; rather, patience, self-control, discretion (how a man spares his soul from troubles by being careful about what he divulges, and to whom!!!) and wisdom all must be evident, but not ostentatiously paraded. But they must not be sole replacements for quintessentially youthful attributes either, but rather work in harmony with them. If you profess abhorrence for any genre of music 22 year olds listen to, whether or not she likes it, you run the risk of appearing unyouthful. Do not, however, at all costs, pretend to be into things she likes when you actually have no interest in them. If you don't like them, don't say so and don't say you do; just be "easy" about them.
Also, play sports, excel at them, dress and groom as youthfully as you feel comfortable with (don't overdo it), but in no wise verbally point any of your qualities out to her. These are things that a woman has to notice for them to be of any worth; as they were wont to say in Scotland of old concerning certain experiences, "it's better felt than tell't", and indeed, a woman has to FEEL you are the great man you would like her to believe you are, rather than be told so, or at least, told so by you.
When in her company, tease her gently (but NEVER insult her, even jokingly) just as you would with any other girl you would flirt with, as there is an unspoken sexual expression in adeptly poised teasing that says you are virile, you notice her womanliness, and you are therefore not a dull older guy. Also, be gentlemanly without making any reference to it, but again, don't be overly overt about it - few guys her age possess that quality, and while few girls her age will rate that as a desirable attribute in a man, it nonetheless is a mark of maturity and manliness she should associate with your age, and if you can do it without being a Beta wimp nice guy type in the process, I think it may prove to be a plus point, albeit a lesser one. Overall, the key is, I suppose, to always be pleasant and friendly in a measure and manner that leaves her wondering if you fancy her or not.
Girls of 22 will expect a man of 32 to be financially stable (not filthy rich, just secure), not living at home with his parents (that's me in trouble then!) and in possession of a very cogent reason for being unattached at that age (in my case, I wasted nearly 7 years on a fiancee I eventually split up with).
In all of this, you must be very measured in how you deal with her. You may be a deep and sensitive person, but very few 22 year old girls will appreciate any display of this. They also tend to be full of the joys of spring, as it were, thinking they have their whole lives ahead of them. They are on the proverbbial "first wonder" ("I wonder who I'll marry?"), convinced they have options aplenty. Alas, before they know it they are headed for the second wonder ("I wonder who'll marry me?"), around their mid 20s (a good age to catch a single girl, especially if she's been available for more than a few months). You wouldn't want (well, I wouldn't want) a woman on her 3rd wonder ("I wonder will ANYONE marry me?"), as by then they are losing the flower of feminine allure...
But I digress. A girl of 22 can be won, I am certain. I just feel it may require more patience than would be the case for babes your own age. I wish you well, my friend, and don't be discouraged if you make mistakes along the way to this girl's heart, as perfect Don Juan performances just don't exist. At least if you do make the odd faux pas, she will probably be too inexperienced herself to catch on to how bad it was!