Preheat the oven to 350°F (175°C) and line 2 rimmed baking sheets with parchment paper.
Remove 2 tablespoons (15 g) of the instant banana pudding mix and set it aside for the frosting.
1 (3.4 oz / 96 g) box instant banana pudding mix
In a large bowl, use an electric mixer to cream the granulated sugar, brown sugar, and softened butter for 1 to 2 minutes, until light and fluffy.
1 cup (200 g) granulated sugar, ½ cup (110 g) light brown sugar, ½ cup (113 g) unsalted butter
Add the mashed banana, egg, egg yolk, and vanilla extract. Mix until smooth and fully combined.
1 medium ripe banana, 1 large egg, 1 large egg yolk, 1½ tsps (7.5 ml) vanilla extract
Add the remaining pudding mix, flour, baking powder, and sea salt. Mix just until combined, then scrape the bottom and sides of the bowl with a rubber spatula. The dough will be thick.
2½ cups (300 g) all-purpose flour, 1½ tsps (6 g) baking powder, ½ tsp (3 g) fine sea salt
Use a 2-tablespoon (30 ml) cookie scoop to portion the dough onto the prepared baking sheets.
Refrigerate the scooped dough for at least 1 hour or overnight. Chilling helps the cookies bake thicker and spread less. I prefer an overnight chill.
Bake for 11 to 14 minutes, until the edges are lightly golden and the centers still look slightly soft.
Immediately swirl a round cookie cutter or small bowl around each warm cookie to smooth the edges, then gently flatten the tops with the bottom of a measuring cup.
Cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Meanwhile, place the butter in a small skillet over medium-low heat. Cook, stirring frequently, until it turns deep golden brown and smells nutty, about 6 to 8 minutes. Let it cool for several minutes.
½ cup (113 g) unsalted butter
Beat together the browned butter, confectioners' sugar, softened cream cheese, reserved pudding mix, and vanilla extract until smooth and fluffy.
2¾ cups (330 g) confectioners' sugar, 4 oz (113 g) full-fat cream cheese, reserved 2 tbsps (15 g) instant banana pudding mix, 1 tsp (5 ml0 vanilla extract
If the frosting is too thick, mix in 1 to 2 tablespoons (15 to 30 ml) milk. If it's too soft, beat in additional confectioners' sugar ¼ cup (30 g) at a time until it reaches a spreadable consistency.
1-2 tbsps (15-30 ml) milk
Spread or pipe the frosting onto the cooled cookies.
If desired, top each cookie with a mini vanilla wafer and a fresh banana slice just before serving. To help slow browning, dip the banana slices in a little lemon juice or pineapple juice before placing them on the cookies.
20 mini vanilla wafer cookies, 1-2 bananas sliced, 1-2 tbsps (15-30 ml) lemon juice or pineapple juice