Bring a large pot of salted water to a boil. For al dente pasta, follow the instructions on the package. Drain the pasta but keep about ½ cup of pasta water set aside.
While the pasta is cooking, season the chicken pieces generously with salt and pepper. Heat a large skillet over medium-high heat and add a tablespoon of olive oil. Brown the chicken for 2-3 minutes per side. Put the chicken on a plate and loosely tent with foil.
Using the same skillet, add the remaining olive oil and garlic and stir for about 30 seconds. Pour in the chicken broth and lower the heat, bringing the broth to a low simmer.
Add the Boursin cheese and cherry tomatoes. Break up the cheese and mix until it melts into the broth, creating a sauce. Mix in the Parmesan cheese.
Add the spinach, pasta and chicken back into the skillet. Gently toss everything until it’s coated in the sauce and the spinach wilts. Add some pasta water to loosen the sauce up, if necessary.
Remove the skillet from heat and stir in the lemon juice. Serve the pasta into bowls and sprinkle with extra Parmesan cheese.