2 tablespoons olive oil
1 large shallot, minced
1-2 large cloves garlic, minced
1 pound mixed mushrooms, such a bella, cremini, or shitake, sliced
3-4 sprigs fresh thyme
1/2 cup dry white wine, such as Sauvignon blanc
9 large eggs, lightly beaten
2 cups whole milk
1 cup heavy cream
2 tablespoons Dijon mustard
2 teaspoons kosher salt
Freshly ground black pepper
1 pound (16 ounces) cubed French bread, day old or toasted
1 (8-ounce) round of brie, rind removed and cut into 1/2-inch cubes
1/4 cup freshly grated Parmesan
Kosher salt and freshly ground black pepper