Instructions

Adjust oven rack 6 inches from broiler element and heat oven to 350 degrees. Bring 2 pounds onions, halved and sliced through root end ¼ inch thick; 3 tablespoons extra-virgin olive oil; ¼ cup water; 1 tablespoon packed brown sugar; 2 teaspoons minced thyme; and ¾ teaspoon table salt to boil in 12-inch skillet over medium-high heat. Cover and cook, stirring occasionally, until water has evaporated and onions are softened and lightly browned, 6 to 8 minutes. Uncover and continue to cook, stirring often and scraping up any browned bits, until onions are well browned, 6 to 10 minutes longer. 
Stir in ½ cup sherry, scraping up any browned bits, and cook over medium heat until evaporated, about 3 minutes. Sprinkle onions with 3 tablespoons all-purpose flour and cook, stirring constantly, for 1 minute. Stir in 2½ cups chicken broth, ½ cup heavy cream, ½ teaspoon pepper, and ¼ teaspoon salt, scraping up any browned bits, and simmer, stirring often, until thickened, about 2 minutes. Cover skillet; reduce heat to medium-low; and simmer, stirring occasionally, until mixture has consistency of thin gravy, about 20 minutes. Remove skillet from heat.
Meanwhile, toss 8 ounces baguette, cut into 1-inch cubes; remaining 3 tablespoons oil; remaining ¼ teaspoon salt; and remaining ¼ teaspoon pepper together on rimmed baking sheet. Bake until golden and crisp, 15 to 18 minutes. Let croutons cool on sheet.
Heat broiler. Crack 1 egg into small bowl, then pour egg into center of skillet over gravy. Repeat with remaining 7 eggs, spacing them evenly around perimeter of skillet. Return mixture to simmer over medium heat. Cover skillet; reduce heat to medium-low; and cook, rotating skillet as needed to ensure even cooking, until whites are set and mostly opaque, 4 to 6 minutes. 
Off heat, sprinkle croutons evenly over egg mixture, followed by 1½ cups shredded fontina and ⅔ cup shredded Parmesan. Broil until cheese is melted, about 1 minute. Serve immediately.