This is a great fresh but surprising omelet. My family raises chickens, and I love recipes that showcase their egg's fantastic flavor and color. It is important to use a sweet tomato in the relish because it really complements the creaminess of the omelet and the lime's tartness. —Goldilocks
Mix the eggs and half and half with a fork gently in a bowl.
In a heavy medium sized non-stick skillet, melt butter and reduce the heat to low, add eggs, then cheese, then avocado, cook until it becomes somewhat firm (10-15 minutes) and then fold gently to create the omelet. The secret to a light and delicate omelet is low heat!
Meanwhile assemble the relish by cutting the cherry or grape tomatoes in half. Season with salt and fresh pepper, toss with lime juice, add cilantro, and serve as a garish with half the omelet.