Preheat the oven to 350°F. Line a 9x13-inch baking pan with foil or parchment paper and spray with cooking spray.
For the brownies: Cut the butter into tablespoon-sized pieces. Add the butter and chocolate chips to a medium microwave-safe bowl. Microwave for 30 seconds, then stir. Repeat for 15-second intervals, stirring each time, until the chocolate and butter are completely melted and well-combined.
Add the sugar, vanilla and salt to the chocolate mixture. Whisk to combine.
Add the eggs one at a time, whisking until each one is fully incorporated.
Using a rubber spatula, mix in the gluten-free flour until fully combined.
Pour the batter into the prepared baking pan. Smooth into an even layer. Bake for 30-35 minutes, until set and a toothpick inserted into the center of the brownies comes out clean.
Remove from the oven and place the pan on a wire rack to cool completely before topping.
For the fudge frosting: In a small saucepan over medium heat, melt the butter. Add the milk, granulated sugar, vanilla and salt and bring to a boil. Boil for 45 seconds.
Remove from the heat and stir in the chocolate chips until smooth.
Working quickly, pour the frosting over the brownies and spread into an even layer. Top generously with sprinkles.
Let the frosting set completely before slicing. I usually refrigerate the brownies for an hour or so to get cleaner slices.