Place turkey bacon in a large non-stick skillet over medium-high heat. Cook, turning once, until nicely browned, about 4 minutes. Transfer to a plate. Pour eggs into the same skillet and cook, lifting edge of egg from pan with a spatula and tilting so that uncooked egg runs underneath. When mostly set, flip over and cook another 30 seconds. Remove from heat.
Toast English muffins while still warm, place chees on bottom half.
Add tomato and basil. Divide egg into 4 pieces and place on tomato. Top with turkey bacon and mashed avocado. Place remaining muffin half on top. Serve immediately.
Large avocados are recommended for this recipe. A large avocado averages about 8 ounces. If using smaller or larger size avocados adjust the quantity accordingly.