Preheat the oven to 350°F. Line an 8x8 baking pan with parchment paper and lightly grease it.
In a medium saucepan over low heat, melt the butter and semi-sweet chocolate chips together, stirring often until smooth. Remove from the heat and let it cool slightly.
Whisk the maple syrup, eggs, and vanilla extract into the melted chocolate mixture until smooth.
Stir in the oat flour, cocoa powder, and salt until just combined. The batter should be thick and glossy.
Pour the brownie batter into the prepared pan and spread it evenly. Drop spoonfuls of creamy peanut butter over the top, then gently swirl it into the batter with a butter knife or toothpick.
Bake for 25-30 minutes, or until the edges are set and the center no longer jiggles. A toothpick inserted near the center should come out with moist crumbs.
Let the brownies cool completely in the pan before lifting them out and slicing into squares.
Do not over mix the batter: Stir just until the oat flour, cocoa powder, and salt are combined so the brownies stay soft and fudgy.
Use creamy peanut butter: Creamy peanut butter works best for swirling. If using natural peanut butter, make sure it is very well stirred so it does not separate or leave oily spots.
Do not over bake: Pull the brownies when the edges are set and the center no longer jiggles. A toothpick should come out with moist crumbs, not completely clean.
Let them cool completely: Gluten-free brownies need time to set, so let them cool before slicing for the best texture.
Use certified gluten-free oat flour: If you need the recipe to be fully gluten-free, make sure your oat flour is labeled certified gluten-free.