In a medium bowl, whisk together the flour, baking soda, baking powder, and salt. In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and granulated sugar on medium-high speed until light and fluffy, 3 to 5 minutes.
Decrease the mixer speed to medium-low and add the eggs, one at a time, beating well and scraping the bowl after each addition with a rubber spatula. Add the vanilla and mix to combine. Add half of the flour mixture, then the sour cream, and then the other half of the flour mixture, mixing only until the last bit of flour disappears. The mixture will seem more like cake batter than cookie dough. Cover the bowl with plastic wrap and refrigerate for 2 hours or overnight. The dough will keep in the refrigerator for up to 3 days.
Preheat the oven to 350°F [180°C]. Line two baking sheets with parchment paper.
As best you can (the dough will be very sticky and soft), portion out a tablespoon of dough with a small cookie scoop or measuring spoon, and evenly place 12 on each of your prepared sheets. Sprinkle the balls with extra rainbow sprinkles. Place in the freezer for at least an hour.
Bake one sheet at a time for 9 to 11 minutes, rotating at the halfway point, until lightly browned around the edges. Let cool slightly on the sheets before transferring to a wire rack to cool completely. Repeat with the remaining cookie dough. The jumbles can be stored in an airtight container on the counter, for up to 3 days, but they will noticeably soften each day.