Preheat oven to 375 degrees. In a mixing bowl, whisk together flour, baking powder and salt, set aside. In the bowl of an electric mixer, fitted with the paddle attachment, cream together butter, granulated sugar and light-brown sugar on medium-low speed until well blended, about 1 minute. Mix in egg and vanilla. Add sour cream and mix until blended.
With mixer on low speed, slowly add in dry ingredients and mix just until incorporated. Scoop dough out 1 even tablespoon at a time and with buttered hands roll dough into a ball. Place balls on cookie sheet (you can fit 15 per sheet but then you are left with 4 in the end so unless you were making a double batch it wouldn't matter to try and fit that many).
Bake in preheated oven 14-15 minutes until bottoms are lightly golden brown. Transfer cookies to a wire rack to cool. Allow cookies to cool completely then spread about 1 teaspoon of peach jam evenly across the bottom of one cookie then gently press another cookie over the jam layer to sandwich them together. Repeat this process with remaining cookies.
To decorate cookies, pour 3 tbsp of milk into two small bowls. Tint one bowl of milk with red food coloring until it reaches a vibrant pink, then tint the other bowl of milk with yellow food coloring until its reaches a vibrant yellow. Take a paint brush and dip into the yellow tinted milk then paint randomly across both cookies leaving some areas unpainted.
Then dip paintbrush into red tinted milk and paint randomly across unpainted areas and blend slightly (tip: I found the less milk I was able to paint across the cookie the better because then your cookies won't become soggy. You really don't need very much at all). Immediately after painting cookie, dip and coat entire cookie with sugar. Insert one or two fresh mint leaves into the side of each cookie if desired. Store in an airtight container.