Preheat oven to 375°F and line baking sheets with parchment paper.
Beat butter and both sugars until light and fluffy, then beat in eggs and vanilla.
Stir in flour, baking soda, and salt until just combined, then fold in chocolate chips.
Flatten about 2 tablespoons dough; place one marshmallow and one chocolate square in the center. Wrap dough around filling and roll into a ball.
Place on prepared baking sheets at least 3 inches apart and bake for 11 to 13 minutes until edges are golden but centers look slightly underdone.
Cool on the pan for 5 minutes before moving to let the marshmallow set.