Preheat oven to 375°
Heat the skillet on medium-high, add olive oil and watch until it shimmers.
Add sausage and break it up into small bits with a spatula or large spoon. Cook until evenly browned. Turn down the heat if this seems to be happening too fast.
Mix in onions and saute for 3-5 minutes, until softened, but not brown.
While the onions cook, break eggs into large bowl and whisk in heavy whipping cream until you have a nice, smooth mixture.
To the skillet, add garlic, red pepper flakes (if used), and half the basil. Mix in and cook a minute.
Lightly butter or grease the baking dish.
Add half the meat and veg mixture to the baking dish. Spread evenly.
Add half the grated cheese (4 oz) as a layer in the baking dish.
Add the rest of the meat-veg and then the rest of the cheese to the dish.
Slowly pour the egg-cream blend (eggs and cream like this is what custard is) over the stuff in the baking dish.
Top the casserole with the sliced tomatoes and the rest of basil.
Into the oven for 35-40 minutes. Check after 30 minutes and keep checking until the jiggling just about stops. Remove from oven and place on an empty burner or better, on a cooking rack for 15 minutes. A bit of baking will continue to happen for a while. Then the casserole will cool and become easier to cut.
I think cutting into six pieces makes for good-sized servings. I use a spatula with a sharp edge for this.