Start by boiling some salted water and add the penne. You want it to cook until it's al dente, feeling slightly firm to the bite. Stir occasionally so it does not stick together.
While the pasta is cooking, season the chicken breasts with salt and pepper. Dredge them lightly in flour so they get that lovely crust later.
Grab a large skillet and heat up the olive oil and butter over medium heat. You will know it's ready when the butter is melted and starts to foam.
Add the chicken to the hot skillet and let it cook for about five minutes on each side, until golden and cooked through. Check for doneness and avoid cutting into the chicken too soon.
Once the chicken is done, toss in the minced garlic and stir it around for about a minute until it's fragrant.
Pour in the chicken broth, lemon juice, Dijon mustard, and Italian seasoning, then stir everything together. Let it simmer for a couple of minutes until it slightly thickens.
Slowly pour in the heavy cream, stirring gently until combined. Do this on low heat to prevent the cream from curdling.
Stir in the fresh baby spinach and grated Parmesan cheese until the spinach wilts and the cheese melts.
Finally, add the drained pasta into the skillet, tossing everything together gently.