Preheat the oven to 350°F. Spray two mini muffin tins with nonstick spray.
Roll each slice of bread to about 1/8-inch thickness with a rolling pin, brush both sides with melted butter and cut each into 4 equal squares. Reserve any remaining butter for cooking the mushrooms.
Press each buttered bread square into the muffin tins to form a small cup. Bake for 6 to 8 minutes, or until lightly toasted. Remove from the oven and set aside.
While the toast cups bake, clean and trim the mushrooms, then chop them finely into 1/4-inch pieces.
Heat the olive oil and any remaining butter in a large pan over medium-high heat. Add the garlic and onion and sauté until soft and fragrant, about 2 minutes. Add about half of the mushrooms, season with salt and pepper and continue cooking until they release some liquid and shrink slightly. Add the remaining mushrooms and more salt and pepper.
Continue cooking, stirring occasionally until all liquid has evaporated and the mushrooms are nicely browned, 8 to 10 minutes. Stir in the white wine and thyme leaves and cook until the wine has evaporated completely, about 3 minutes longer. Taste and adjust seasoning if necessary.
Spoon the mushroom mixture into the prepared toast cups and top each with a piece of muenster cheese. Bake until the cheese is melted and bubbly.