1. Place the butter in a small saucepan and heat over medium-low heat until completely melted and browned, stirring frequently. About 5 minutes. Be careful, don’t burn the butter. Transfer the butter into a large bowl and let cool to room temperature.
2. In a small bowl stir flour, baking soda and salt. Set aside.
3. To the bowl with brown butter and both sugars and beat until light and fluffy. Add eggs, one at the time and vanilla, beat just until combined, about 15-20 seconds. Gradually add flour mixture, stir just until combined. Fold in the chocolate chips.
4. Chill the dough in the refrigerator for 30 minutes.
5. Preheat oven to 360F (180C).
6. Scoop out about 1-2 tablespoons of cookie dough and flatten it, spoon 1-1½ teaspoons of peanut butter (chilled) in the center, roll into a ball.
7. Place rolled balls on a parchment paper with about 2 inches apart.
8. Bake for 10-12 minutes or until lightly browned on the sides. Cool on baking sheets for a 10 minutes before transferring to wire racks to cool completely.