Preheat the oven to 375°F (190°C).
Grease a large sheet pan or line it with parchment paper.
In a large bowl, whisk together eggs, milk or cream if using, oregano, thyme, salt, and black pepper until combined.
Add any desired mix-ins such as bell peppers, spinach, cooked bacon, ham, or shredded cheese to the egg mixture and stir to incorporate.
Pour the egg mixture evenly onto the prepared sheet pan and smooth the surface with a spatula.
Bake for 12 to 15 minutes until the eggs are set but still moist; avoid overbaking.
Allow the baked eggs to cool slightly, then use a round cutter or glass rim to cut egg rounds that fit your sandwich buns or English muffins.
Use the egg rounds immediately to assemble breakfast sandwiches with cheese, bacon, sausage, avocado, or preferred toppings.