Preheat the oven to 350 degrees F. Toss the tomatoes with the thyme, olive oil and 1/2 teaspoon each salt and black pepper in a bowl. Spread on a baking sheet and roast, stirring once or twice, until the tomatoes are slightly dried and browned in spots, 1 hour to 1 hour, 15 minutes. Cool completely.
Whisk the milk, eggs, fontina, 3/4 cup parmesan, the cayenne, 1 teaspoon salt and 1/4 teaspoon black pepper in a large bowl. Add the bread cubes and greens and toss to coat. Pour into a 3-quart baking dish, then top with the roasted tomatoes. Cover and refrigerate overnight.
The next day, preheat the oven to 350 degrees F. Sprinkle the strata with the remaining 1/4 cup parmesan and bake, uncovered, until golden brown and almost set, about 45 minutes. Turn off the oven, but keep the strata inside 10 minutes before serving.
Photograph by Tina Rupp
Recipe courtesy Food Network Magazine