Cut broccoli florets into small pieces. Slice one floret into at least 3 pieces. Cook your chosen favorite pasta in salted water. I recommend cooking the pasta al dente. Drain the cooked pasta and rinse it with cold water to stop the cooking process. At the end of cooking the pasta, save some water – about half a cup – as it may come in handy later.
In a pan, melt butter and add finely chopped or grated garlic cloves. Sauté for about half a minute, then pour in the cream and broth. Add dried thyme, pepper, and salt. Stir everything together. Once the cream with broth comes to a boil, add broccoli pieces and simmer covered for about 5 minutes. Cook for a few more minutes for the sauce to thicken properly.
Next, add the previously cooked pasta and mix everything well. Finally, sprinkle with grated Parmesan or Grana Padano cheese. You can also add finely chopped parsley. If necessary, you can add pasta water.