Position a rack about 6 inches from the broiler and preheat. Cook the bacon in a large (12-inch) ovenproof nonstick skillet over medium-high heat until crispy, about 8 minutes. Transfer to a paper towel-lined plate and crumble the bacon when cool. Add the potato, 1/2 teaspoon of salt, paprika, and basil and cook, stirring occasionally, until the potato is brown and tender, about 8 to 10 minutes.
Meanwhile, whisk the eggs and milk with the remaining 1 teaspoon salt and black pepper to taste.
Add the shrimp and bacon into the skillet and stir until the shrimp are pink, about 1 minute. Pull the skillet from the heat, pour the eggs over the potatoes and shrimp. Stir, just until the eggs begin to set and the potatoes and shrimp are evenly distributed in the skillet. Scatter the cheese over the eggs and top with the red pepper. Broil the tortilla until the eggs are set and the cheese begins to brown, about 2 to 3 minutes. Serve from the skillet. Alternatively, use a rubber spatula to loosen the eggs from the side of the skillet and invert onto a plate, invert the tortilla again, onto a serving platter or invert and slide tortilla onto a cutting board. Slice into wedges and serve garnished with cheese and parsley.
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