Melt butter in a saucepan over medium heat; cook and stir often, 6 minutes until brown in color; keep stirring so it does not burn; remove from heat and let sit for 5 minutes to cool
Pour butter into an electric mixer with paddle attachment; while the butter is still hot, add both sugars; mix on low until combined; let sit to cool for a few minutes
Mix in the eggs and vanilla; mix in the baking soda and salt; slowly mix in flour until mixture is just combined; stir in chocolate chips
Line a cookie sheet with parchment paper; scoop 2 tablespoon balls of cookie dough; wrap one peanut butter cup in each ball of cookie dough then roll between hands to completely conceal
Place balls on cookie sheet; cover cookie sheet with plastic wrap; chill for a minimum of 4 hours
Preheat oven to 350F; place cookies 2″ apart on cookie sheets; bake for 12-15 minutes until just starting to turn brown; cool for 5 minutes before removing