Preheat oven to 350 degrees and line a 9x9 baking pan with nonstick foil. In microwave, melt butter.
Stir in sugar and vanilla extract. Add eggs, one at a time, and incorporating each egg in before adding another one. Stir in the dry ingredients. Pour half the batter into the prepared baking pan and place Reese's cups next to each other. Pour the rest of the batter on top of the Reese's cups, covering them. Spread the batter gently with an offset spatula to make sure everything is covered.
Bake for 35-40 minutes then remove from oven and let brownies cool in pan until room temperature.
Chill and then trim into squares.