Preheat oven to 350 degrees. Line 2 baking sheets with parchment. Sift flour, baking powder, baking soda, and salt into a bowl. Combine banana and sour cream in another bowl.

Beat butter and granulated and brown sugars with a mixer on medium-high speed, until pale and creamy, about 3 minutes. Add egg and 1/2 teaspoon vanilla, beating until incorporated. Add banana mixture in 2 additions, alternating with flour mixture.

To make the round cookies, you can use a pastry bag or even a pancake pen to pipe them into perfect circles, or you can use a small cookie scoop for slightly less perfect rounds.

Bake until edges are golden, about 12 minutes. Slide parchment, with cookies, onto wire racks. Let cool. (Unfilled cookies can be stored for up to 1 day.)

Beat cream cheese, confectioners’ sugar, and remaining 1/2 teaspoon vanilla with a mixer on medium speed until smooth, about 2 minutes.

Pipe or spoon 1 tablespoon cream cheese mixture onto the flat sides of half the cookies. Sandwich with remaining cookies. Dust with confectioners’ sugar and serve immediately.