Use a sharp pair of kitchen shears or a non-stick knife to cut all of the red and green gumdrop candies cleanly in half, then set them aside in a small bowl. Line an 8×8-inch or 9×9-inch square baking dish with a large sheet of parchment paper, ensuring the excess paper hangs up and over the outer edges to act as handles later.
Bring a medium saucepan filled with 1 to 2 inches of water to a steady boil on your stovetop, then lower the burner to maintain a gentle simmer. Place a large, completely dry, heat-proof glass or stainless steel bowl directly on top of the saucepan to create a double boiler, making absolutely sure the bottom of the bowl does not touch the bubbling water below.
Drop the melted unsalted butter, both bags of mini marshmallows, and both bags of white chocolate chips directly into the heat-proof bowl over the indirect steam. Stir the ingredients continuously with a heat-resistant silicone spatula for 5 to 7 minutes as the steam gently coaxes the chocolate lipids and marshmallow gelatin to break down, melding them into a completely smooth, thick, and uniform white paste before pulling the bowl entirely off the stove.
Let the hot white chocolate matrix cool on the counter for 3 to 4 minutes until it is warm to the touch but no longer scalding, then gently fold the halved colorful gumdrops into the mixture until they are evenly speckled throughout. Waiting for this brief cooling window is crucial because dumping gelatin-based gumdrops directly into a boiling hot sugar mixture will cause the candies to melt, bleed their artificial food dyes, and turn your clean white nougat into a muddy, streaky mess.
Scrape the sticky gumdrop nougat directly into your prepared parchment-lined baking dish, using a second piece of lightly oiled parchment paper pressed firmly flat against the top surface to smoothly push and level the dense mixture into the corners.
Remove the top parchment sheet and leave the pan undisturbed on the counter overnight to allow the melted gelatin and cocoa fats to fully recrystallize and firm up into a chewy, resilient sliceable candy block.
Firmly grasp the overhanging edges of the parchment paper handles and lift the set nougat block straight out of the baking dish onto a sturdy cutting board.
Run a long, serrated kitchen knife under hot tap water for 15 seconds, dry the blade completely on a clean towel, and slice the nougat into uniform, bite-sized bars. Wipe the blade clean and re-warm it under hot water between every single cut to cleanly slice through the sticky marshmallows and dense chocolate without tearing the edges.