Combine flour, baking powder, baking soda, and salt in a bowl and set aside—this keeps your dry ingredients ready and ensures the leavening agents are evenly distributed. In a large mixing bowl, beat the softened butter and granulated sugar together for about 3 minutes until the mixture is light and fluffy, which incorporates air for a tender crumb. Add the room temperature eggs one at a time, then mix in the sour cream and vanilla extract until fully combined. Gently fold in the dry ingredient mixture until just combined—avoid overmixing, which can make cookies tough. Divide the dough in half, wrap each portion in plastic wrap, and refrigerate for at least 4 hours or freeze for 1 hour; chilling relaxes the gluten and prevents excessive spreading during baking.
Preheat your oven to 350°F and line your baking sheets with parchment paper while the dough chills. Lightly flour a clean work surface for rolling the chilled dough.
Working with one portion of chilled dough at a time, roll it out to about 1/4-inch thickness on your floured surface. Cut out shapes with your cookie cutter and place them on the prepared baking sheets, spacing them about 2 inches apart to allow for gentle spreading. Bake for 10-12 minutes until the cookies are set but still slightly soft in the center—they should not be browned, just pale golden. I find that slightly underbaking these cookies keeps them tender and moist, which is the hallmark of a great sour cream cookie.
Allow the baked cookies to cool on the baking sheet for 5 minutes—this helps them set and firm up slightly. Then transfer them to a wire rack to cool completely before frosting. This two-stage cooling prevents breakage and ensures even frosting application.
While cookies cool, beat the softened butter, sifted confectioners' sugar, vanilla extract, salt, and light corn syrup together until smooth and creamy. Add milk gradually, one tablespoon at a time, beating until you reach your desired consistency—I prefer a spreadable frosting that's not too stiff or too runny. The corn syrup adds shine and prevents the frosting from being chalky.
Spread or pipe the frosting from Step 5 onto the cooled cookies. Add sprinkles or other decorations immediately if desired, while the frosting is still slightly wet so they adhere properly.