Add the flour, sugar, baking powder, and salt to a medium bowl. Stir together to combine.

Add the softened butter and work the dough through your fingers until everything is well combined and incorporated. The dough should feel crumbly, almost like wet sand, and should lightly hold its shape when pressed together.

Add the egg and mix it with your hands until it is well combined with the dough.

Add the warm milk and vanilla extract and combine with your hands. Knead the dough for 5 minutes on a well-floured surface until the dough forms a smooth ball, adding more flour to the surface as needed. The dough should be tacky but not totally sticky.

Cover with a clean kitchen towel and let it rest for 10 minutes.

Uncover and form the dough into 10 balls.

Place 2 pieces of parchment paper on a tortilla press to keep it from sticking. Place the dough ball on top of the parchment paper and press the balls into 5-inch gorditas.

Heat a large skillet or comal over medium heat. Place a gordita in the skillet and cook for 3-4 minutes on each side until small brown spots begin to form. Place the cooked gorditas in a tortilla warmer to keep them soft and pillowy.

Serve immediately.