Sweet and Savory Bread Pudding

Name: Sweet and Savory Bread Pudding
Ingredients: 2 tablespoons butter, plus extra for greasing the pan; 1 pound butternut squash, peeled, and cut into 3/4-inch pieces; 4 parsnips, peeled, and cut into 3/4-inch pieces; Kosher salt for seasoning; Freshly ground black pepper for seasoning; 1 (1 pound) loaf brioche, challah, or sourdough bread, cut or torn into 1-inch pieces; 3 cups heavy cream; 8 eggs, beaten; 3/4 cup brandy; 1/4 cup vegetable oil; 3 tablespoons brown sugar; 2 tablespoons cinnamon; 1 tablespoon fresh thyme leaves, chopped