Preheat oven to 350°F (180°C). Line rimmed baking sheets with parchment paper.

In the bowl of a stand mixer fitted with the paddle attachment, beat butter and sugar at medium-high speed until light and fluffy, 3 to 4 minutes, stopping to scrape bottom and sides of bowl and paddle. Add egg and extract, beating until combined.

In a medium bowl, whisk together flour, pudding mix, baking soda, and salt. With mixer on low speed, gradually add flour mixture to butter mixture, beating just until combined. Stir in sprinkles.

Using a 3-tablespoon spring-loaded scoop, scoop dough (about 64 grams), and place 2 inches apart on prepared pans.

Bake until edges are set but centers still look a little gooey, 10 to 11 minutes. Let cool on pans for 5 minutes. Remove from pans, and let cool completely on a wire rack. Store in an airtight container for up to 4 days.