Preheat your oven to 350°F (175°C). Grease or line an 8x8 inch baking pan with parchment paper.
In a mixing bowl, combine the gluten-free flour, cocoa powder, baking powder, salt, and granulated sugar. Stir until well combined.
Add the vegetable oil, unsweetened applesauce, non-dairy milk, and vanilla extract to the dry ingredients. Mix until a smooth batter forms. If you're using chocolate chips, fold them into the batter at this stage.
In a small microwave-safe bowl, heat the peanut butter in the microwave for about 30 seconds until it's slightly softened and easier to swirl.
Pour about two-thirds of the brownie batter into the prepared baking pan, spreading it out evenly. Then, drizzle spoonfuls of the softened peanut butter over the brownie batter.
Use a knife or a toothpick to gently swirl the peanut butter into the brownie batter, creating a marbled effect.
Pour the remaining brownie batter over the peanut butter layer, spreading it out evenly to cover the peanut butter swirl.
Place the baking pan in the preheated oven and bake for 25-30 minutes, or until the edges are set and a toothpick inserted into the center comes out with a few moist crumbs (but not wet batter). Be careful not to overbake.