I know I have read somehwere, you can take mint leaves, wash very well, crush them or chop fine to bruise them, then place in a jar with equal amounts leaves as vodka. (ex: 1c mint to 1c vodka). This should probably sit for at least a month... then you can strain it well and use. I may be wrong, but it said to pick them during the day... and leave the jar in a sunny area...
You could try chopping some leaves VERY finely and adding them to the batter - but I suspect the results won't be quite satisfactory in baking. The bits of leaves will add an odd texture. Or you could make a VERY strong tea and add a bit to the recipe, perhaps two or three times as much as the amount of extract the recipe calls for; consider it part of the liquid in your recipe and adjust accordingly. But you'd probably do better to just get a small bottle of peppermint extract and keep it in the cupboard with your vanilla extract.
The thing about growing mints - they are so exuberant! Even in a container, they grow and grow. You might dry some of the leaves (pick them in the early morning of a dry day; you can just lay them on a wire sieve and turn them a bit till they dry - keep them out of sunlight) and store in a glass jar. Tea for the winter. And be sure to add fresh leaves in your cooking! A nice note with some vegetables.
I was wondering if it is possible and how I would go about substituting fresh sweet mint for peppermint extract in baked goods in general (though the recipe I'm thinking of is a light(er) brownie recipe). I've got this pot of mint on my balcony growing absolutely wild and I would like to make something besides tea out of it!