Bring a large pot of salted water to a rolling boil. Add the penne pasta and cook until al dente, about 10-12 minutes. Reserve ½ cup of pasta water, then drain and set aside.

Heat 2 tablespoons of olive oil in a large skillet over medium-high heat. Season the chicken with salt and pepper, then cook for 6-7 minutes on each side until golden-brown. Transfer to a plate and let it rest before slicing.

In the same skillet, sauté the minced garlic for about 30 seconds until fragrant. Add the broccoli and stir-fry for 3-4 minutes until bright green and tender-crisp.

Pour in 1 cup of heavy cream and 1 cup of chicken broth, stirring to combine. Let simmer for 2-3 minutes, then gradually add Parmesan cheese until melted.

Add the cooked penne and sliced chicken to the skillet, tossing to coat them evenly with the sauce. If the sauce is too thick, add a splash of reserved pasta water.

Remove from heat, stir in lemon juice, and adjust seasoning with salt or pepper. Serve immediately, garnished with extra Parmesan cheese.