Preheat the oven to 350°F (175°C). Lightly grease a 9×13-inch baking dish.
Line a baking sheet with parchment paper or foil. Arrange the turkey ham strips in a single layer and set aside.
In a large bowl, whisk together the eggs, milk, red bell pepper, green bell pepper, green onion, cilantro, ½ cup of the shredded cheese, and freshly ground black pepper.
Pour the egg mixture evenly into the prepared baking dish. Place both the egg mixture and turkey ham in the oven.
Bake the eggs for about 15–20 minutes, or until completely set. Heat the turkey ham until lightly browned around the edges. Cooking time can vary depending on its thickness.
Place the English muffin halves in the oven during the final 3–4 minutes so they become lightly toasted.
Meanwhile, prepare the chipotle sauce. Add the chipotle pepper, adobo sauce, garlic, yogurt, and cilantro to a food processor or blender. Blend until smooth and creamy, then season with salt.
Remove the baked eggs from the oven. Use a round cookie cutter or knife to cut four portions approximately the same size as the English muffins.
To assemble the Chipotle Egg Scramble Breakfast Sandwiches, place one baked egg portion onto the bottom half of each toasted English muffin.
Sprinkle with the remaining cheese, add a generous spoonful of chipotle yogurt sauce, and top with two strips of warm turkey ham. Add fresh cilantro if desired.
Finish with the remaining English muffin halves and serve warm.