Sourdough Strata With Tomatoes and Greens

plum tomatoes, quartered lengthwise

chopped fresh thyme

extra-virgin olive oil

Kosher salt and freshly ground black pepper

whole milk

large eggs

Italian fontina cheese, grated (about 3 cups)

grated parmesan cheese

cayenne pepper

loaf sourdough bread, cut into 1-inch cubes (about 8 cups)

chopped greens, such as kale, spinach or arugula