Lightly grease an 8 x 8-inch (20 x 20 cm) baking pan with the softened butter. Line the bottom and sides with parchment paper, leaving enough overhang on two sides to lift out the chilled nougat.

Place the gumdrops in a large mixing bowl: If any are larger than about 1/2 inch (1.25 cm), cut them in half. Toss them with 1 tablespoon (8 g) of the powdered sugar until lightly coated and less sticky.

Place the chopped white baking chocolate and 2 tablespoons (28 g) butter in a heavy-bottomed saucepan. Set over the lowest burner heat.

Stir continuously for 3 to 5 minutes, until the chocolate is mostly melted and smooth. Do not allow the mixture to simmer or become very hot. If the chocolate begins sticking to the pan, remove it from the heat briefly while continuing to stir.

Add the mini marshmallows to the melted chocolate: Continue cooking over very low heat for 3 to 5 minutes, stirring constantly, until the marshmallows melt into the mixture.

Once fully combined, the mixture should be thick, glossy, stretchy, and smooth with no large marshmallow pieces remaining. Remove the pan from the heat immediately.

Stir in the vanilla extract and salt until evenly incorporated.

Let the nougat mixture stand for about 3 minutes, stirring once. It should remain soft and spreadable but no longer be extremely hot. This helps keep the gumdrops from softening excessively.

Add the powdered sugar-coated gumdrops and fold gently until they are distributed throughout the nougat. Avoid prolonged stirring, which can cause their colors to streak into the white mixture.

Scrape the mixture into the prepared pan: Lightly butter the spatula or place a piece of parchment over the surface, then press the nougat into an even layer reaching all four corners.

Remove the top parchment, if used, and smooth the nougat as evenly as possible. Sprinkle the remaining 1 tablespoon (7 g) powdered sugar lightly over the surface.

Cover the pan and refrigerate for at least 4 hours. The nougat should feel firm when pressed but remain slightly flexible rather than hard.

Use the parchment overhang to lift the chilled nougat onto a cutting board. Peel away the parchment carefully.

Use a sharp knife to cut the slab into 6 equal strips in each direction, creating 36 squares. Wipe or lightly butter the knife between cuts if the nougat begins sticking.

Let the pieces stand at room temperature for about 5 minutes if you prefer a softer chew, or serve them directly from the refrigerator for a firmer texture.