Preheat oven to 350ºF.
In medium-sized bowl, combine the sugars and the melted butter. Add the vanilla and mix well.
In a separate bowl, sift together the dry ingredients (flour, cocoa powder, baking powder, and salt).
Alternate adding the wet and dry ingredients to the butter mixture. The easiest way to do this is to add half of the sifted dry ingredients, then add the wet ingredients (coffee and nondairy milk), and then add the remaining dry ingredients. Fold together until just combined.
Fold in the chocolate chips and pour into a parchment-lined 8"x8" baking pan. Swirl the peanut butter into the top of the brownie batter (I usually melt the peanut butter, then pour it in lines or squiggles over the top of the brownie batter, then use a knife to swirl it together).
Bake until the brownies are set along the outside but still a little bit wet in the middle, about 30-35 minutes. Taking the brownies out before they're fully done is what gives brownies that fudgy texture!