Prepare your oven and pan by preheating the oven to 350°F / 175°C. Generously grease 10 wells of a standard 12-well muffin pan with oil or non-stick spray.
In a medium skillet over medium heat, cook the breakfast sausage and dried chives. Use a spoon to crumble the meat as it cooks until it's browned and cooked through, which should take about 10 minutes.
Drain off any excess fat and set the sausage aside.
In a medium bowl, whisk the 6 large eggs until smooth.
Add the heavy cream, oregano, salt, and pepper, and whisk again until everything is well combined. Gently stir in the cooked sausage mixture and the shredded cheddar cheese.
Carefully pour the egg mixture into the 10 prepared muffin wells, filling each one about three-quarters of the way to the top to allow for rising.
Bake for 15 to 20 minutes, or until the centers are firm to the touch and the tops are lightly golden brown.
Let them cool slightly before removing from the pan. Store leftovers in an airtight container in the refrigerator for up to 5 days.
