Snap the tenerumi stems where they stop bending easily and discard the thick, stringy lower parts. Wash the leaves and shoots in three changes of cold water, then chop everything into 5 cm / 2-inch pieces. Break the spaghetti into 3 to 4 cm / 1 1/2-inch pieces and boil a kettle of water.
Warm the olive oil and garlic in a 28 cm / 11-inch Dutch oven (5-quart / 4.7 L) over medium-low heat for 1 minute, until the garlic is pale gold and fragrant. Add the tomatoes and red pepper, raise the heat to medium, and cook for 4 minutes, pressing with a wooden spoon, until the tomatoes collapse and release their juice.
Add the tenerumi in handfuls, stirring until each batch wilts, about 2 minutes in total. Pour in the 1 L / 4 1/4 cups of just-boiled water, add the salt, and bring back to a boil. Partly cover and simmer for 8 minutes, until a stem is tender when you bite it.
Stir in the spaghetti and push it under the liquid. Simmer uncovered over medium heat for 9 minutes, stirring every minute or two, until the pasta is al dente and the broth is slightly thick. If the pot tightens before the pasta is done, add 60 ml / 1/4 cup of hot water at a time.
Taste and adjust the salt. Ladle into warm, wide bowls and top with the pecorino, black pepper, and a drizzle of olive oil. Serve within 10 minutes of finishing.