Put the Parmesan, oil, lemon juice, sun-dried tomatoes, 3 tablespoons water, vinegar, 1/2 teaspoon salt and a few grinds of pepper in a jar or other container with a lid. Secure the lid, and shake vigorously to combine. (The dressing can be made a day ahead; shake well before serving.)
Lay the bacon in a large nonstick skillet, and cook over medium heat until golden and crispy, about 5 minutes per side. Drain on paper towels, then finely chop.
Wipe out the skillet, coat with cooking spray and heat over medium heat. Crack the eggs into the skillet, and cook until the whites are set but the yolks are still runny, 4 to 5 minutes. Sprinkle the eggs with salt and pepper. Remove from heat.
Meanwhile, toast the bread, then rub one side of each slice with the garlic. Cut each slice in half. Put 2 toast halves on a plate, and top each set with a romaine heart half. Drizzle with the dressing, top with an egg and sprinkle with bacon. Repeat with the remaining toast, romaine, dressing, eggs and bacon.
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