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Step 1
Cook the Pasta and Broccoli - In a large pot, bring water to a boil. Add 1 ½ teaspoon salt, and stir to dissolve. Add the pasta and cook until al dente, about 10 to 12 minutes, or according to the manufacturer's directions. A few minutes before the pasta is ready, add the broccoli florets. Cook until bright green and tender, about 2 to 3 minutes. Reserve 1 cup of starchy water to make the cream sauce. Drain the pasta and broccoli.
Step 2
Prepare the Chicken - Cut the chicken breast into about 1-inch cubes—season with 1 teaspoon salt and ¼ teaspoon pepper.
Step 3
Cook the Chicken - Heat a large skillet over medium heat. Once the pan is hot, add 2 tablespoons of olive oil. Add the chicken in a single layer, and cook without moving until the surface is golden brown, about 2 to 3 minutes per side. Transfer to a clean bowl.
Step 4
Saute the Garlic - Heat the same skillet used to cook the chicken and adust to low heat. Add 1 tablespoon olive oil and minced garlic, and saute until fragrant, 30 seconds.
Step 5
Reduce the Cream - Stir in the heavy cream, chicken stock, ½ teaspoon salt, and ½ teaspoon black pepper. Bring to a simmer over medium heat. Frequently scrape the sides and bottom of the pan to ensure the cream does not curdle. Reduce the sauce until it just starts to thicken and lightly coats the back of a spoon, about 5 to 6 minutes.
Step 6
Finish the Sauce - Turn off the heat and stir in the parmesan cheese, lemon zest, and lemon juice. If the sauce is too thick, add the reserved pasta water, 1 tablespoon at a time, until you reach the desired consistency—season with salt and pepper to taste.
Step 7
Combine and Stir - Add the pasta, broccoli, and chicken to the sauce, gently stirring to combine.
Step 8
To Serve - Serve the meal garnished with chopped parsley.