A few of my Italian friends think that chicken in pasta is gross and stupid, and that is totally inexplicable to me. Meaty ragus are commonplace in Italy, so I’m not sure why chicken in pasta is taboo. My vote is that we just go ahead and put chicken in our pasta and not worry about what anybody thinks of it. This pasta (with chicken) is unlike any weeknight pasta you’ve ever had. It’s a nod toward cacio e pepe, but instead of making a sauce from the pasta cooking liquid and black pepper, we are using garlicky chicken stock with a subtle hint of cinnamon and star anise. There is also the roast chicken and charred broccoli and fresh herbs to make it feel like we’re not just eating pasta for the millionth night in a row—not that there’s anything wrong with that!
In a roasting pan, combine the broccoli, garlic, chicken breasts, oil, and 2 teaspoons of the salt. Toss everything well and spread out evenly in the pan. Roast for about 20 minutes, or until the broccoli is a little charred on the edges, the garlic is a little brown, and the chicken is no longer pink. Pull the pan out of the oven and put the chicken on a plate to cool. Put the roasted garlic in a large sauté pan.
In a large pot, boil enough water to cook the pasta. Add the pasta to the boiling water and cook for about two-thirds of the time recommended on the package (5 to 6 minutes).
While the pasta is cooking, add the stock, cinnamon, star anise, and remaining 1 teaspoon salt to the pan with the garlic, bring it to a boil, and lower the heat to a simmer. Shred the cooked chicken.
Drain the par-cooked pasta (reserving some of the cooking water) and add it to the pan with the stock. Increase the heat to high and cook the pasta for another 5 to 6 minutes, stirring regularly. When the pasta is a minute away from being done, add the broccoli and chicken and stir well to combine. The pasta will have absorbed some of the liquid and the stock will have reduced, but there should still be a cup or so of liquid in the pan; if not, add some pasta cooking water or chicken stock.
Turn off the heat and add the butter, Parmesan, and herbs, stirring well until the butter and cheese are melted. Remove and discard the cinnamon and star anise before serving.