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, dried oregano, dried thyme, salt, and black pepper until combined.
Add any desired mix-ins such as diced bell pepper, chopped spinach, cooked bacon or ham, or shredded cheese and stir to combine.
Pour the egg mixture evenly onto the prepared sheet pan and smooth the surface with a spatula.
Bake for 12 to 15 minutes, until eggs are set but still moist. Avoid overbaking.
Allow the eggs to cool slightly, then use a round cutter or glass rim to cut rounds that fit your sandwich buns or English muffins.
Serve immediately as breakfast sandwiches with your favorite toppings or store for later.