These gluten-free brownies are so super-fudgy and rich that it's hard to stop eating them. They're just as good cold as at room temperature. Slideshow: More Brownie Recipes
Preheat the oven to 350°. Lightly grease a 9-by-13-inch metal baking pan.
Place the 3 sticks of butter in a heatproof bowl and set the bowl over a saucepan of simmering water (the bottom of the bowl should not touch the water). Melt the butter, stirring occasionally. Add the chopped chocolate and stir until melted. Remove the bowl from the heat.
In a small bowl, whisk the rice flour with the tapioca flour and salt. In a large bowl, whisk the eggs with the sugar and vanilla until blended. Fold in the dry ingredients until incorporated, then fold in the peanut butter chips and chocolate chips. Fold in the melted chocolate mixture. Scrape the batter into the prepared dish.
Bake for about 1 hour and 15 minutes, until the brownies are slightly puffed and a tester inserted in the center of the brownies comes out with a few moist crumbs attached. Transfer the pan to a rack and let cool completely before turning out the brownies and cutting them into bars.
The brownies can be stored in an airtight container at room temperature for 3 days, or wrapped in foil and frozen for up to 1 month.