Rinse broccoli and divide into florets. Blanch in boiling salted water for about 3 minutes. Drain and rinse in cold water, drain well.
Peel onion and garlic, chop onion and slice garlic. Heat olive oil in a nonstick skillet and saute broccoli, onion and garlic briefly. Remove broccoli from the pan and keep warm.
Add vegetable stock and cream to the pan and bring to a boil. Grate cheese, add to the pan and melt, stirring. Season with salt and pepper.
Cook pasta shells in boiling salted water according to package instructions until al dente. Drain well. Toss pasta with broccoli and sauce. Arrange on plates and serve.