Mix the dry ingredients. Whisk the flour, baking powder, baking soda, and salt in a large mixing bowl until evenly combined. Set aside.
Cream the butter and sugar. In a separate bowl, beat the butter and sugar with an electric mixer on medium-high speed until light and fluffy, about 3-5 minutes. The mixture should appear pale and creamy. Then, add the eggs, one at a time, beating well after each addition. Next, mix the sour cream and vanilla extract, blending at medium to low speed until smooth.
Combine the wet and dry ingredients. Slowly add the dry ingredients to the wet mixture, 1 cup at a time, mixing at low speed until combined. The dough will be very soft—this is normal.
Chill the dough: Cover the bowl with plastic wrap or transfer the dough to an airtight container. Refrigerate for at least 1 hour or until firm enough to handle.
Preheat the oven and prepare the baking sheets. Preheat your oven to 375°F (190°C). Then, line baking sheets with parchment paper or lightly grease them with cooking spray.
Shape and bake. Using a tablespoon or small cookie scoop, drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart. For a smoother look, gently roll the dough balls in your hands. Bake for 10-12 minutes until the edges are lightly golden and the tops appear set. If baking multiple sheets at once, rotate them halfway through the baking time for even cooking.
Cool the cookies. Remove cookies from the oven and let them cool on the baking sheet for 5 minutes. Then, transfer to a wire rack to cool completely before glazing.