Preheat a large sauté pan and add a tablespoon of oil. Add to hot pan diced ham, shallot, and tomato. Sauté over medium heat for 7 to 8 minutes until tender and reduced. Remove from heat and set aside.
In large bowl, whisk together the eggs and milk, season with salt, pepper and herbs. Add the sautéed mixture to the eggs, along with the chives, and half of the cheese.
Heat a medium sized frying pan and add 1 tablespoon oil. Pour in the egg mixture. Stir slowly for the first minute, then turn heat down to low, cover with lid and let the top almost set, about 8 minutes. Carefully, fold omelette in half and cook for addition 2 to 3 minutes. Remove from heat and onto plate. Sprinkle with remaining cheese and top with slices of heirloom tomato and avocado.