Prepare pineapple bun topping first by combining softened butter with sugar until smooth.
Add 1 egg yolk and vanilla extract and mix.
Fold in flour, baking soda, and baking powder until combined. Wrap the dough in plastic wrap and roll into an even log. Freeze for 15 to 20 minutes to firm up.
Brown the butter by placing it in a saucepan over medium heat. As soon as you notice the melted butter turning a light brown, remove the heat and continue stirring as the color darkens.
Whisk the flour, baking soda, and salt together in a bowl.
Add the white sugar and brown sugar to the brown butter. Using a mixer, beat together until combined. Add in the egg and vanilla extract.
Pour dry ingredients into the wet ingredients and beat together. Roll 1 tablespoon of dough into balls.
Cover with plastic wrap and place in the refrigerator to chill for 30 minutes.
Preheat the oven to 350°F. Line large baking sheets with parchment paper.
Cut pineapple bun topping into small sections that you can roll into balls. Usually these balls will be the size of a quarter (roughly).
Roll each ball out into a ¼ inch thickness between 2 sheets of parchment paper. Place topping over each ball of cookie dough. The topping should cover ¾ of the cookie dough ball.
Brush with a simple egg wash made by beating one egg in a small bowl.
Place cookie dough balls about 3 inches apart from each other on a baking sheet.
Bake for 12–13 minutes or until lightly browned.
