¾ cup shredded Swiss cheese (½ cup plus ¼ cup for topping)
8 whole eggs
½ teaspoon kosher salt
¼ teaspoon black pepper
Heat oven to 375°F.
Heat butter in a 10-inch non-stick, oven safe sauté pan over medium high heat. Add onions to the hot pan and sauté in butter for 5-7 minutes or until edges of onions just start to brown. Reduce the heat to medium low and sprinkle with a ¼ tsp kosher salt, garlic and fresh thyme leave. Let cook for 25-30 minutes, stirring occasionally. If the onions begin to crisp, add a few tablespoons of water to the pan and reduce the heat.
While the onions are cooking, beat the eggs with the salt and pepper. Add ½ of a cup of the Swiss cheese, reserving ¼ cup for later.
When the onions are completely soft and a deep golden color, raise the heat to medium and add the ham to the pan. Cook for 1 minute, until the ham is heated through.
Pour the egg mixture into the pan and stir with a spatula until the everything is combined, and the eggs start to set, about 30 seconds. Without stirring, let the eggs continue to cook for 4-5 minutes. While the eggs are cooking, check the side to make sure they aren’t browning. If they are, reduce the heat.
When the eggs are completely set on the bottom and starting to set on top sprinkle with the remaining ¼ cup Swiss cheese and move the pan to the oven. Cook for 6-8 minutes until eggs are completely set and lightly browned. Remove from the pan, cut into 6 wedges, and serve.