Bring a pot of salted water to a boil. Cook the broccoli in the boiling water according to the package instructions. Drain, then cut into small florets.
Slice the prosciutto in half lengthwise to make long strips. Line each cup of a 12-cup muffin pan with 2 strips of prosciutto arranged in an X pattern. Fold the overhang back into each cup and lightly press to cover any gaps or holes. Hold in the refrigerator.
Heat the olive oil in a medium skillet over medium heat. Add the onion and saute until softened, about 5 minutes. Add the crushed red pepper and garlic, then season with salt and pepper. Cook until the garlic is softened, another 2 minutes. Remove from the heat and let cool to room temperature, about 15 minutes.
Preheat the oven to 400 degrees F.
In a large bowl, whisk together the milk, cream and eggs and season with a pinch of salt and pepper. Mix in the cooled onion and garlic mixture and the Parmesan. Divide the broccoli among the prosciutto-lined muffin cups. Pour some of the egg mixture into each cup, filling each about three-quarters full.
Bake until the quiches are set, 15 to 17 minutes. Let cool for 5 minutes before removing them from the muffin cups. Serve warm.