Peel the baked sweet potatoes, dice into ½-inch cubes, and place in a small bowl with the brown sugar. Stir to combine well. Peel the baked white potato, dice into ½-inch cubes, and set aside.
Whisk the eggs in a medium-size bowl until frothy, then blend in the milk or cream.
In a 10-inch ovenproof skillet with 2-inch sides, heat ¼ cup of the fat or oil over medium-high heat until hot, 1 to 2 minutes. Add the Tasso and white potatoes and cook, stirring occasionally, for 1 minute. Add the onions, bell peppers, and Meat Magic, and cook, stirring occasionally and scraping the pan bottom well, for 3 minutes. Stir in the squash and zucchini and continue cooking, stirring occasionally and scraping the pan bottom well, for 3 minutes. Stir in the sweet potatoes and cook and stir for 2 minutes more. Remove from heat and set aside.
In a separate skillet, heat the remaining fat or oil over medium heat until hot. Whisk the egg mixture briefly again and add it to the skillet, making sure to cover the entire bottom of the skillet. As soon as the eggs begin to firm on the edges, add the reserved vegetable mixture to one side of the omelet, saving about ¼ cup of the mixture for garnish. Cook for 1 to 2 more minutes. Fold the other side of the omelet over the vegetable mixture and cook 1 or 2 more minutes. Garnish the top of the omelet with the reserved ¼ cup of vegetable mixture. Serve immediately.