Fluffy Sugar Cookies with Royal Icing/Sprinkles

2 cups granulated sugar*2 1/2 cups all-purpose flour1/2 tsp baking powder1/2 tsp salt14 Tbsp (1 3/4 sticks) unsalted butter, softened1 Tbsp vanilla extract2 large eggsSpread 1/2 cup of the sugar* in a shallow dish for coating and set aside. In a separate bowl, whisk the flour, baking powder, and salt together and set aside.Beat the butter and remaining 1 1/2 cups sugar together in a large bowl using an electric mixer on medium speed until light and fluffy, 3-6 minutes. Beat in the vanilla, then the eggs, one at a time, until combined, about 30 seconds, scraping down the bowl & beaters as needed.Reduce the mixer speed to low and slowly mix in the flour mixture until combined, about 30 seconds. Give the dough a final stir with a rubber spatula to make sure dough is combined. Refrigerate dough for at least an hour.Adjust oven rack to middle position and heat oven to 350°F. Using palms, roll 2 Tablespoons of dough at a time into balls, then roll in sugar to coat. Place balls on baking sheets, spaced 2 inches apart.Bake cookies, one sheet at a time, until the edges are set and just beginning to brown but the centers are still soft and puffy, 10-12 minutes, rotating the baking sheet halfway through baking. Allow cookies to cook on baking sheet for 10 minutes, then serve warm or transfer to a wire rack and let cool completely.