Place a sauté pan over medium-high heat. Add cooking oil; when hot, add onions and sauté until translucent. Add sausage and cook until brown and crumbly, 8 to 10 minutes. Transfer mixture to paper towels to drain and set aside.

Preheat oven to 350°F. 

Place a large saucepan over medium-high heat; add milk and butter and bring to a low boil. Gradually whisk in grits; reduce heat and simmer, whisking constantly, 5 to 7 minutes or until grits are done. Remove from heat.

Whisk about 1 tablespoon of hot grits into beaten egg; add back to grits along with Cheddar. Combine thoroughly, taste, and add salt and pepper. 

Spread cooked drained sausage evenly in a lightly greased 11x7-inch baking dish. Spread cheese grits evenly over sausage; sprinkle with grated Parmesan cheese.

Cover, transfer to the oven, and bake 35 to 40 minutes or until mixture is set. Increase heat to broil, remove covering, and bake until browned on top, about 5 minutes; do not burn

Makes 8 to 10 servings.

Shortcut: instead of one casserole, prepare this in individual mini-servers; diners can bake their own in the toaster oven at their leisure.