Fill a large saucepan with 2 to 3 inches of water and bring to a boil over high heat. Reduce the heat to medium-low, pour in the vinegar and 2 teaspoons of salt, and keep the water at a gentle simmer.
While waiting for the water to simmer, place a slice of mozzarella cheese and a thick slice of tomato onto each English muffin half, and toast in a toaster oven until the cheese softens and the English muffin has toasted, about 5 minutes.
Crack an egg into a small bowl. Holding the bowl just above the surface of the water, gently slip the egg into the simmering water. Repeat with the remaining eggs. Poach the eggs until the whites are firm and the yolks have thickened but are not hard, 2 1/2 to 3 minutes. Remove the eggs from the water with a slotted spoon, and dab on a kitchen towel to remove excess water.
To assemble, place a poached egg on top of each English muffin. Spoon a teaspoon of pesto sauce onto each egg and sprinkle with salt to taste.