Charcoal Maker's Spaghetti with Fiorets of Broccoli

Our family likes the classic spaghetti alla carbonara, but we also like the exquisite broccoli carbonara and other variations. 

• 400g Spaghetti 
• 1 Head of broccoli 
• 1 Whole egg 
• 3 Yolks 
• 150 g Guanciale or Pancetta
• 1 Garlic glove 
• 40g Pecorino 
• Salt & Pepper (QB)

The preparation is practically the same as the traditional recipe, except boil pasta and broccoli in the same pot. You can use also artichoke, cauliflower, Brussel sprouts, spinach, carrots, or any combination of vegetables. Of course you can also play with other ingredients. Why not replace pecorino with gorgonzola cheese? Can't find guanciale? Use pancetta or bacon! I am sure food fascists would not mind, but they would mind if you mixed in cream, onions, tomatoes, parsley or olives. 

No cream, No tomatoes, No onions, No parsley, No olives!