Louisiana Sugar Cookies

Combine dry ingredients, including flour, sugar, baking powder, and salt, in a large bowl until they are well incorporated. Add cold butter to the mixture and use a spoon or whisk to blend it until the ingredients have a rough, crumbly texture. Introduce beaten egg and yolk, milk, and vanilla into the mixture and stir until it forms a cohesive mass.

Transfer the dough to a lightly dusted work surface and knead it until it comes together in a cohesive ball, requiring 3 to 5 gentle manipulations. Form the dough into a round shape and cover it with plastic wrap, refrigerating it for about an hour to allow it to firm up.

Preheat the oven to 400 degrees F (200 degrees C) and position a rack in the middle of the oven. Line two large, rimmed baking sheets with parchment paper to prepare them for use.

Roll out the dough on a heavily floured surface to an even thickness of 3/8 inch. Use a cookie cutter with a diameter of 2 1/2 inches to cut out cookies, re-rolling the dough as needed if it becomes too small. Place the cookies on the prepared baking sheets, leaving about 1 inch of space between each cookie.

Freeze the cookies uncovered for 15 minutes to firm them up before baking. Bake one tray of cookies at a time in the preheated oven until their edges are golden brown, taking about 10 to 12 minutes. Remove the cookies from the oven and let them cool on the baking sheet for 2 minutes before transferring them to a wire rack to cool completely, about 15 minutes. Repeat the baking process with the remaining tray of cookies.

Store the cooled cookies in an airtight container at room temperature for up to 1 week.