Cacio e pepe beans and broccoli

Cover the dried beans with water and leave overnight to soak.

Next day, drain or not, and cover the beans by a couple of inches of water to keep the starch concentrated.

Bring to a boil with a tight-fitting lid.

Reduce to a simmer, an hour to an hour and a half.

Salt early, one or two teaspoons; add more water if the pot gets dry.

After an hour, when just barely too firm, kill the heat and ladle off about half the beans for another use.

If there is much more liquid than wanted, pour some off or simmer longer to thicken.

Cut the broccoli crown into smallish florets, set them on top of the beans, turn the heat back on, cover and steam while the beans finish.

For the garnish, chop sage leaves and a peeled garlic clove together as fine as possible.

After about five more minutes check the broccoli with a fork; turn the heat off and let it coast.

Grate in a large pile of Pecorino or Parmesan and a lot of black pepper; stir to bring the sauce together. If too thin, add cheese, smash some beans or simmer gently; do not boil hard or the cheese goes gritty.

Sprinkle over the garnish and sage flower petals.