Note: This dough requires chilling!
Melt butter in a saucepan over medium heat. Cook, stirring often, about 6 minutes, until it becomes brown in color. It will foam, reduce, then foam again. Once it’s done cooking the foam is a light brown and it will dissipate after you remove it from the heat. Once it starts to brown, keep stirring so it doesn’t burn. Let sit for about 5 minutes to cool.
Pour butter into an electric mixer fitted with paddle attachment. (You can also use a hand mixer.) While still hot, add both sugars and mix on low until combined. Let sit to cool for a few minutes, then mix in the eggs and vanilla. Mix in the baking soda and salt, then slowly mix in flour until mixture is just combined. Stir in chocolate chips.
Line a cookie sheet with parchment paper or a silicone baking mat. Scoop 2 tablespoon balls of cookie dough and wrap a peanut butter cup in each one, rolling between your hands to completely conceal. Place balls on cookie sheet. Spacing doesn’t matter, you’ll be chilling the dough. Cover cookie sheet with plastic wrap and chill at least 4 hours (but overnight is better.)
Preheat oven to 350°F. Place cookies 2” apart on 2 cookie sheets and bake (while the balls are cold from the refrigerator) for about 12-15 minutes or until they just begin to turn brown and are no longer glossy on top. Cool at least 5 minutes on cookie sheet before removing.
Store in an airtight container for up to 3 days or freeze for up to one month.