Preheat the oven to 325°F. Grease an 8-inch square baking pan and line with parchment paper. Set aside.
First, make the banana pudding mixture. Place all banana pudding ingredients into a medium bowl. Whisk together, using a handheld electric mixer on medium speed, until well combined and smooth, scraping down the bowl as needed. Set aside the banana pudding mixture while you make the brownie batter.
To make the brownie batter, place the butter and ¾ cup of the chocolate chunks in a medium glass bowl, melt together by placing in the microwave for 60 seconds. Stir the mixture, and then place in the microwave for an additional 30-60 seconds to melt completely.
Whisk in sugar, brown sugar, eggs and vanilla extract.
Add gluten free all-purpose flour, cocoa powder and Kosher salt. Stir together until combined.
Spread in the greased pan, and dollop with the banana pudding mixture. Using a butter knife or a small off-set spatula, gently swirl the banana batter and brownie batter together creating a marble effect. Sprinkle the brownie batter with the remaining chocolate chunks and banana chips.
Place in the oven and bake for 25-30 minutes. Remove from the oven, and let cool for 5-10 minutes. Place the pan in the refrigerator on a cooling rack to cool completely, about 2 hours.
Cut into 12 equal pieces before serving.