Bring a pot of water to boil (use enough water to cover the eggs when they lay in the bottom). Drop the metal rims (outer rim only) of two mason jar lids into the pot so they are laying flat on the bottom. When the water is boiling, turn off the heat and carefully crack the eggs directly into each rim. Cover the pot and poach for 5 minutes (4 for super soft, 4:30 for soft, 5 or more for semi-soft yolks).
While the eggs are cooking, toast the bread and smash the avocado on each piece of toast. When the eggs are done, use a spatula to lift the eggs out of the water. Gently pull the rim off of the eggs (Do this right on the spatula, over the water) and place the poached eggs on top of the toast. Sprinkle with Parmesan cheese, salt, pepper, and fresh herbs; serve with the fresh quartered heirloom tomatoes.