In the bowl of a food processor combine the egg, egg yolk, lemon juice, mustard, 1 tablespoon of water, garlic, and Essence and process on high speed for 20 seconds. While the motor is still running, add the vegetable oil and olive oil in a slow, steady stream until the mixture is thickened. If mixture becomes too thick before all of the oil is incorporated, add a bit more water as necessary. Add salt, to taste, and set aside while you assemble the remaining ingredients for the sandwiches.
In a small bowl coat 4 tomato slices evenly with cornmeal and season with salt. In a large heavy skillet, heat 1/2 cup of the reserved bacon drippings until hot but not smoking and cook the tomatoes until golden brown on both sides, about 5 minutes. Transfer to paper towels to drain. Coat any remaining tomato slices and cook in the same manner, adding additional bacon drippings as necessary.
Lightly toast the bread slices. Assemble the sandwiches: spread each slice of bread with the desired amount of mayonnaise. Divide the tomatoes, bacon slices, avocado slices and lettuce leaves between 4 slices of the bread. Top with the 4 remaining slices of bread, with the mayonnaise-spread sides facing inward. Cut in half and serve.
Yield: 4 large sandwiches