This is my easy method for poaching eggs. If you like to poach your eggs a different way, go for it.Fill a pot or deep skillet with 2 inches deep with water. Add 1 tablespoon of vinegar to the water. (Don't worry; your eggs will not taste like vinegar.)Bring the water to a rolling boil and then reduce heat so that it is just barely simmering. There should still be bubbles on the bottom of the pan, but the surface of the water should look calm.
Crack egg into small sieve and allow watery albumin to drain off. (Don’t worry; the white and yolk will stay intact inside the sieve.)
Holding the egg in the sieve just above the water, gently roll the egg out of the sieve and into the water.Leave the egg alone. You can put about four or five eggs into the pan at the same time, but be sure they all have enough room. After about a minute, use a slotted spoon to unstick the egg from the bottom of the pan if necessary.
Allow the egg to cook a minute or two, and then use the slotted spoon to lift it up out of the water and gently poke it with your finger to see if it is done to your liking. If it is, remove it to a plate. If it needs to cook longer, simply lower it back into the water for another minute and check it again.
Position the oven rack to be 6-inches below the heating element. Preheat oven broiler on high.
Spread pesto over the top of each tomato slice, and put the tomato slices on the lined baking sheet. Broil for 4-5 minutes. Remove from oven.
For each serving: A. Start with one or more broiled tomatoes. (You can use one big slice, or stack a few smaller slices.)B. Top tomato(es) with a poached egg.C. Top generously with shredded cheese.D. Sprinkle lightly with paprika and season with salt and pepper as desired.
Pop the assembled eggs-and-tomatoes under broiler for about a minute to melt cheese.