Preheat oven to 350°F. Grease a 9-inch pie plate and set aside.
In a skillet over medium heat, brown the ground beef and sausage. Break up with a wooden spoon into small pieces while cooking. Cook until no longer pink, about 4 to 5 minutes.
Add the spices and salt to the meat and stir to combine. Cook 1 additional minute.
In a large measuring cup, whisk the eggs and half-and-half together.
Transfer the meat to the prepared pie plate and spread into an even layer.
Pour the egg mixture evenly over the meat. Top with the shredded cheese.
Bake for 30 to 35 minutes. Let rest 5 to 10 minutes before serving.