In a medium bowl, mix together the flour, baking soda, baking powder, and salt. Set aside.
In a large bowl, cream together the softened butter, brown sugar, and white sugar with an electric mixer on high speed for 1-2 minutes until light and fluffy.
Add the egg yolks and vanilla. Mix on medium-high speed until light in color and fluffy, about 1-2 minutes.
Add the peanut butter and mix on medium speed until smooth.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until combined.
Scoop the cookie dough into 16 portions using a 2-tablespoon cookie scoop. Roll each portion into a ball and press the center with a 1-teaspoon measuring spoon to create an indent. Chill the dough balls on a parchment-lined baking sheet for one hour.
Preheat the oven to 350°F.
Arrange 6 cookies per parchment-lined baking sheet. Bake for 10-11 minutes.
When the cookies come out of the oven, press the centers again with a ¼-cup measuring cup to deepen the indent and use a circular cookie cutter to round the edges.
Let the cookies cool on the baking sheet for 5 minutes, then transfer to a cooling rack to cool completely.