Preheat oven to 350°F (175°C).
Toss bread cubes with 2 tablespoons olive oil and garlic salt. Spread on a baking sheet and toast for 10-15 minutes, or until golden brown.
In a large pot, melt butter and remaining 2 tablespoons olive oil over medium heat. Add onion and cook until softened, about 5 minutes. Add garlic and cook for 1 minute more.
Add mushrooms and cook until browned, about 5-7 minutes. Add chard and cook until wilted, about 3-5 minutes.
In a bowl, whisk together honey and wine until honey dissolves.
Layer half of the toasted bread cubes, mushroom mixture, and remaining bread cubes in the pot. Pour honey-wine mixture over the top. Pour broth over everything. Sprinkle with 1 cup grated cheese.
Cover the pot with foil and seal around the edges. Cut 5 vent holes in the top. Bake for 1 hour 15 minutes.
Serve immediately, garnished with remaining cheese, pepper, and thyme.