Position an oven rack in the bottom half of the oven, and preheat to 375 degrees F. Line a rimmed baking sheet with parchment paper.
Whisk together 1 of the eggs, the mustard, 1/2 teaspoon salt, 1/4 teaspoon pepper and granulated garlic in a shallow dish. Mix together the breadcrumbs and 1/4 cup of the Parmesan in another shallow dish.
Toss the asparagus with the flour in a medium bowl. Dip the asparagus in the egg mixture, shake off excess egg, coat the asparagus in the breadcrumb mixture (pressing it in if needed) and transfer to the prepared baking sheet. Bake until the asparagus is tender and slightly browned about 20 minutes.
Crack the remaining 4 eggs into individual cups. Heat the oil in a large nonstick skillet over medium heat, then gently pour as many of the eggs into the pan as you can without crowding. Fry the eggs until the whites have set and the yolks are still runny, about 4 minutes.
Pool 1/4 cup marinara sauce on each of 4 serving plates. Evenly divide the asparagus among them, and top each with an egg. Sprinkle with the remaining 1 tablespoon Parmesan, and garnish with basil.
Never leave a child unattended in the kitchen. Limit the child to tasks that are safe and age-appropriate.
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