Heat oven to broil. Pour water into a shallow sauté pan to measure 1 inch deep. Add vinegar and bring to a simmer.
In small saucepan, combine hollandaise mix, milk and butter. Cook, whisking over medium heat until thickened, 3 to 4 minutes. Remove from heat and cover.
Line a microwave-safe plate with paper towels. Add 4 slices of the turkey bacon and cover with a second layer of towels. Repeat layering. Microwave 2 minutes. Keep warm.
Meanwhile, crack an egg into a small bowl; slip egg into simmering water. Repeat with 3 more eggs. Cook 4 minutes, or until desired doneness. Remove with a slotted spoon to a paper towel-lined plate. Repeat with the 4 remaining eggs.
Toast muffins under broiler for 3 minutes and then put both halves on a plate. Top muffin half with 1 slice of bacon, halved, a piece of roasted pepper, 1 egg and a spoonful of hollandaise sauce (refrigerate remaining sauce). Season with black pepper and serve.