Preheat the oven. Preheat oven to 375°F and position the racks to the upper-middle and lower-middle positions. Line 2 large baking sheets with parchment paper and set aside.
Whisk the dry ingredients. In a medium bowl, whisk together the flour, baking powder, and salt until thoroughly combined; set aside.
Cream the butter and sugar. In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar at medium speed until light and fluffy, about 2 minutes, scraping down the bowl and paddle once.
Add the egg and flavorings. Mix in the egg and vanilla on medium speed until thoroughly combined, about 30 seconds, then add the strawberry gelatin and mix until combined, 20-30 seconds.
Alternate flour and milk. Add half the flour mixture and mix on low until just combined, then mix in the milk, then the remaining flour mixture until no streaks of flour remain.
Scoop the batter. Using a ¼-cup scoop or measuring cup, scoop batter onto the prepared baking sheets, spacing 2 inches apart.
Bake the cookies. Bake for 12-14 minutes, until set and lightly browned on the bottom, rotating pans and switching shelves halfway through baking.
Cool completely. Let the cookies set 1-2 minutes on the baking sheets, then transfer with a thin spatula to a wire rack to cool completely, about 30 minutes.