Put the Parmesan, oil, vinegar, sun-dried tomatoes, lemon juice, 3 tablespoons water, 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, turning once, until golden and crispy, about 5 minutes per side. Transfer to a paper-towel-lined plate to drain, then finely chop.
Wipe out the skillet, coat it with cooking spray and place 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 the 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 each of 4 plates and top each plate with a romaine heart half. Drizzle with the dressing, top with an egg and sprinkle with the bacon. Sprinkle with parsley if desired.
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