Preheat the oven to 325 F.
Chop the rosemary into fine pieces.
In a large skillet, season the ground beef with salt and pepper and rosemary. Then brown the beef well and break it into chunks. Set aside in a bowl.
As the beef is cooking, chop the zucchini and onions. When beef is cooked and set aside in a bowl, add the zucchini and onions to the hot skillet and brown. Add a bit of butter if there is not enough fat left over from the beef to cook them. When cooked, add it in the bowl with the beef.
In a medium bowl, whisk the eggs, cream, salt, and pepper together, mixing well.
Fold the beef, zucchini, and onions into the egg mixture.
Butter or oil the quiche dish. Then sprinkle about 1/2 of the cheese evenly in the bottom of the dish.
Pour the egg and beef mixture into the quiche dish and add the remaining 1/4 cup mozzarella on top of the egg and beef mixture. (Add more grated cheese on top if you wish.)
Bake for 30-40 minutes, until the quiche is just set in the center. Use your nose. You will smell right when it is ready. But let the timer be your backup. Remove from oven and cook on a wire rack at least 10 minutes before serving.