1 ounce dried porcini mushrooms (about 1 cup), broken in half if large
2 cups boiling water
4 ounces French baguette, cut into 3/4-inch cubes (about 3 cups)
3 tablespoons unsalted butter, plus more for coating the baking dish
1 tablespoon olive oil
8 ounces chanterelle mushrooms, stems trimmed and cut in half
8 ounces cremini mushrooms, stems trimmed and cut in half or quartered if large
1/3 cup small-dice shallot (from about 1 medium shallot)
3/4 teaspoon finely chopped fresh thyme leaves
1/2 cup dry white wine
Kosher salt
Freshly ground black pepper
1 large egg, lightly beaten
1/2 cup heavy cream
6 ounces Cambozola cheese, cut into small pieces (rind included)