Bring a large pot of salted water to a boil and cook the pasta until al dente, following the package directions. The pasta should still have a little bite since it will finish in the sauce.

Cut the chicken into bite-size pieces, season with salt and pepper, and coat the pieces lightly with flour. The flour should form a thin, even layer rather than a heavy crust.

Heat the butter and olive oil in a skillet over medium-high heat, then add the chicken and cook until the outside is no longer pink before transferring it to a plate. You want light browning on the edges without fully finishing the chicken at this stage.

Take the skillet off the heat and add the garlic, chicken broth, lemon juice, Dijon mustard, and Italian seasoning, then return it to the burner and let it bubble briefly while scraping the pan. The garlic should smell fragrant, and the browned bits should loosen into the liquid for deeper flavor.

Return the chicken to the skillet and pour in the cream, then add the spinach and simmer for about 5 minutes. Keep the bubbling gentle so the sauce thickens without breaking, and cook until the spinach is wilted and the chicken is fully done.

Drain the pasta, add it to the skillet, and stir in the parmesan until the sauce coats the noodles evenly, then season with more salt and pepper if needed. The sauce should be thick enough to coat the back of a spoon and cling to the pasta instead of pooling underneath.