Arrange a rack in the middle of the oven and heat to 425°F. Gently melt 1 cup (2 sticks) unsalted butter in a saucepan or in the microwave and let it cool while you mix the dry ingredients.
Place 3 cups all-purpose flour, 1 cup granulated sugar, ½ cup packed dark brown sugar, 1 teaspoon baking soda, ½ teaspoon kosher salt, ¼ teaspoon ground cinnamon, and ¼ teaspoon ground nutmeg in a large bowl and whisk to combine; set aside. Whisk 3 large eggs and cooled butter together, then whisk in 1 teaspoon vanilla extract. Pour the egg mixture into the flour mixture and stir just until a soft dough forms.
Place ¼ cup granulated sugar, 1 tablespoon ground cinnamon, and ¼ teaspoon ground nutmeg in a soup plate or shallow bow and whisk to combine. Form the dough into 1 ½-inch balls, then roll each ball completely in the cinnamon sugar. Place 12 of them on an unlined, ungreased baking sheet and flatten slightly.
Bake until set, about 7 minutes. Cool on the baking sheet for 5 minutes. Transfer to a wire rack and cool completely. Repeat baking the remaining dough, letting the baking sheet cool completely between batches.
