Start by lining a 9×13 pan with parchment paper, giving it a light mist of nonstick cooking spray, and setting it aside.
In a big pot, melt the butter over medium heat. Keep stirring until the butter starts to brown slightly – watch out for the foaming and nutty aroma. Remove it from heat immediately to avoid burning.
Stir in two teaspoons of vanilla extract, letting the mixture bubble up until the sizzling subsides. Whisk in the salt.
Add half of your marshmallows, stir until almost completely melted, then add the rest. Keep stirring until all the marshmallows are fully melted.
Now, add the Reese's Puffs, 2 cups at a time, folding with a silicon spatula until combined. Continue until everything is evenly mixed.
Pour the mixture into the prepared 9×13 pan. Use lightly wet hands to gently press it to the edges without crushing it.
In a heatproof bowl, melt the chocolate chips in the microwave (30 seconds, stir, repeat until melted). Set aside for 3 minutes to cool to room temperature.
Using a spoon, drizzle the melted chocolate over the treats. Sprinkle on the chopped Reese's Cups, and you're ready to enjoy your delightful, no-bake dessert!