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Take the broccoli florets out of the freezer and allow them to thaw. When they are soft enough to cut, chop them into smaller, bite-sized pieces. Set the broccoli aside to fully thaw until you are ready to use them.
Bring a large pot of water to boil for the pasta. Once boiling, add the pasta and continue to boil until the pasta is tender. Drain the pasta in a colander.
While the water for the pasta is heating, season both sides of the chicken thighs with a pinch of salt and pepper. Heat a deep skillet over medium flame, then add the olive oil. Tilt the skillet to coat the surface in oil, then add the chicken thighs. Cook the thighs on both sides until golden brown and cooked through (about 5 minutes each side). Remove the thighs to a cutting board and let rest.
While the chicken is cooking, zest the lemon using a zester or small-holed cheese grater and mince the garlic. Once the chicken has been removed from the skillet, turn the heat down to medium-low, and add the garlic. Sauté the garlic for 1-2 minutes, or just until it is soft and fragrant.
Add the chicken broth to the skillet and stir to dissolve all the browned bits off the bottom of the skillet. Add the heavy cream, about 1 tsp of the lemon zest, and 2 Tbsp of the lemon's juice. Stir to combine, and allow the cream to come up to a gentle simmer. Simmer the sauce for a few minutes, or until it thickens slightly. Taste the sauce and adjust the salt, pepper, or lemon if needed. Season the sauce liberally so the flavors are not diluted once combined with the pasta, broccoli, and chicken.
Chop the cooked chicken into small pieces, then add it to the cream sauce in the skillet along with the drained pasta and chopped broccoli florets. Stir to combine and coat everything in sauce. Allow the chicken, broccoli, and pasta to heat through, then serve.