Wash and dry all produce. Preheat oven to 450 degrees. (TIP: For an extra crispy flatbread crust, place a lightly oiled baking sheet in oven as it heats.) Halve, peel, and slice shallot from root to stem end into thin strands. Slice tomato crosswise into thin rounds. Pick basil leaves from stems; discard stems.

Heat a drizzle of oil in a large pan over medium-high heat (use a nonstick pan if you have one). Add sausage and shallot. Cook, tossing, until sausage is browned and cooked through and shallot is translucent, 6-8 minutes. Remove from pan. Cut sausage into 1/2-inch rounds.

Place flatbreads on a lightly oiled baking sheet. Evenly sprinkle with Italian cheese. Season with salt, pepper, and Italian seasoning. Scatter shallot, tomato, and sausage over top, then sprinkle with Parmesan.

Bake flatbreads in oven until crust is golden brown and cheese is melted and bubbly, about 8 minutes.

Wipe out pan used for sausage, then heat a drizzle of oil in it over mediumhigh heat. Gently crack eggs into pan. Cook sunny-side up to desired doneness, 3-5 minutes.

Top flatbreads with eggs, then slice into pieces. Season with salt and pepper. Scatter basil over top and serve.