Melt the butter in a saucepan over medium-high heat. Add the mushrooms and sweat, stirring occasionally, about 5 minutes.
Add the garlic and sauté, stirring often, until mushrooms are browned and all liquid has evaporated, about 15 minutes.
Preheat the broiler. Spread the mustard evenly on one side of each piece of bread.
Top each slice with a sprinkle of cheese, then evenly top with the mushrooms, and finish with another generous sprinkle of cheese.
Broil until the cheese is melted and starting to brown, about 2 minutes.
To serve, sprinkle with fresh thyme and season with salt and pepper.