Preheat oven to 350°. Line baking sheets with parchment paper.
For cookies: In a large bowl, beat butter, sugar, and vanilla with a mixer at medium speed until fluffy, 3 to 4 minutes, stopping to scrape sides of bowl. Add eggs, one at a time, beating well after each addition.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Gradually add flour mixture and milk to butter mixture, beating at low speed until combined. Using a 1½-tablespoon spring-loaded ice cream scoop, drop batter 3 inches apart on prepared pans.
Bake until golden brown, about 12 minutes. Let cool on pans for 3 minutes. Remove from pans, and let cool completely on wire racks.
For filling: In a medium bowl, beat pudding mix, milk, and cream with a mixer at medium speed until very thick, about 2 minutes. Cover and refrigerate for 1 hour.
Spread about 1 tablespoon pudding onto flat side of cookies. Top half of cookies with 3 to 4 banana slices. Place remaining cookies, flat side down, on banana slices; gently press. Serve immediately, or cover and refrigerate for up to 1 hour. Garnish with confectioners’ sugar, if desired.
Recipe by Paula Deen Magazine at https://pauladeenmagazine.com/banana-pudding-whoopie-pies-recipe/