Bring a large pot of salted water to boil over medium-high heat. Blanch broccolini for 2 minutes. Use a slotted spoon to transfer broccolini to a bowl of ice water to stop the cooking. Drain broccolini and set aside. Pour pasta into boiling water and cook until al dente.

Meanwhile, heat a large sauté pan over medium heat and cook pancetta until golden brown. Transfer pancetta to a small bowl, but keep the drippings in the pan. Reduce heat to medium-low and add blanched broccolini and garlic. Add chicken broth and reserved pancetta and simmer.

When pasta is cooked, drain it completely, reserving a cup of pasta water. Turn heat under the sauté pan to medium, then add butter and pasta. Add cheese and toss, adding pasta water a tablespoon at a time to help smooth it out. Finish with sea salt, black pepper, and more grated cheese. Serve immediately.