Line a 8x8 or 9x9 pan with parchment paper.
Using a double boiler pan, melt the butter, chocolate chips, marshmallows and peppermint. Stir until smooth.
Remove from heat and mix in the cut gumdrops.
Pour the mixture into the prepared baking dish, adding a few gumdrops on top.
Allow the nougats to cool and setup by placing in the refrigerator overnight.
Once the mixture has setup, cut into 1-2 inch pieces.
Store in an airtight container with wax paper between the layers.