Heat the oven to 425 F. Place bell peppers in the oven and roast for 10 to 15 minutes until the skin of the peppers begins to bubble and turns brown or black.
Meanwhile, heat a medium saute pan over medium heat and cook the onions for about 6 minutes until caramelized; set aside and keep warm.
Place the peppers in a medium bowl and cover with plastic wrap; set aside. When the peppers are cool to the touch, remove the skin. Cut the English muffins in half and top with cheese, peppers and onions. Place on a baking sheet and bake for about 5 minutes.
To prepare the eggs, first bring the water to a simmer in a medium-sized pan that's shallow and wide. Add the vinegar. Slowly crack the eggs and add to the pan one at a time and cook to desired doneness. Eggs that have runny yolks take about 3 to 4 minutes. Using a slotted spoon, retrieve the eggs from the water. Place an egg on each English muffin half and sprinkle with salt.