Preparation and Dry Ingredients: Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper or silicone baking mats. In a medium bowl, whisk together the all-purpose flour, baking powder, and salt. Set the bowl aside.

Creaming the Fats and Sugars: In the bowl of a stand mixer fitted with the paddle attachment, or using a large bowl and a hand mixer, beat the softened butter, 1 cup of granulated white sugar, and the 1/4 cup of light brown sugar together on medium speed until the mixture is light, fluffy, and pale yellow, about 3 to 4 minutes. Stop the mixer halfway through to scrape down the sides of the bowl.

Adding Wet Ingredients: Add the large egg, the extra egg yolk, milk, and vanilla extract to the creamed mixture. Beat on medium-low speed until the ingredients are just combined, scraping down the sides as necessary. Be careful not to overmix at this stage.

Combining Wet and Dry: Reduce the mixer speed to low. Gradually add the dry ingredient mixture to the wet ingredients, mixing only until the flour streaks have almost disappeared. Stop the mixer just before the dough is fully combined; use a rubber spatula to fold in the remaining dry ingredients by hand to prevent developing too much gluten, which can make the cookies tough.

Chilling the Dough (Optional but Recommended for Chewiness): Cover the bowl with plastic wrap and chill the dough in the refrigerator for 30 minutes. This step helps the cookies hold their shape and ensures a thick, chewy texture.

Shaping and Rolling: Place the remaining 1/4 cup of granulated white sugar into a small, shallow bowl. Scoop the chilled dough using a 1.5 tablespoon cookie scoop (or roll balls approximately 1.5 inches in diameter). Roll each dough ball in the bowl of sugar until it is completely coated.

Baking: Place the sugar-coated dough balls onto the prepared baking sheets, spacing them about 2 inches apart. Bake one sheet at a time for 8 to 11 minutes. The cookies are done when the edges are lightly golden brown and the centers still look slightly soft or puffy. Do not overbake if you desire a truly chewy result.

Cooling: Remove the baking sheets from the oven and let the cookies cool on the sheet for 5 minutes before carefully transferring them to a wire rack to cool completely. Store airtight at room temperature for up to 5 days.