Preheat oven to 350 degrees F.
Bring a large pot of salted water to a boil. Add cauliflower florets and cook until very crisp tender, about 1 minute. Drain in colander and rinse with cold water. Shake off excess liquid.
Heat the oil in a large frying pan, over medium-high heat. Add the ham and the onions and cook until lightly brown, about 6 minutes. Add cauliflower and parsley and set aside to cool slightly.
Brush a 9-inch glass or ceramic pie pan with the soft butter and evenly sprinkle the bottom of the pan with the grated Parmesan Place pan on a baking sheet. Whisk the half-and-half, eggs, egg yolks and flour in large glass measuring cup. Season with salt and pepper, to taste. Spread half the cauliflower mixture evenly in the pan, top with about half the cheese; repeat with remaining filling and cheese. Pour the custard over the fillings.
Bake until the quiche is just set in the center, about 40 to 50 minutes. Cool on a rack before serving.