Bring a large pot of salted water to a rolling boil and cook the spaghetti until al dente (typically 8-9 minutes, but check your package directions). Before draining, scoop out 1/2 cup of the starchy pasta water and set it aside. Drain the pasta, toss with 1 tablespoon olive oil to prevent sticking, and set aside.

While the pasta cooks, let chicken sit at room temperature for 15 minutes for more even cooking. Slice each chicken breast in half horizontally to create thinner cutlets. In a shallow bowl, combine flour, Italian seasoning, lemon pepper seasoning, a generous pinch of salt, and black pepper. Dredge each chicken piece thoroughly in the flour mixture, pressing gently so coating adheres, then shake off any excess.

Heat 1 tablespoon olive oil in a large 12-inch skillet over medium-high heat until it shimmers (a drop of water should sizzle immediately). Add the coated chicken and cook for 4-5 minutes per side without moving them. You want a deep golden-brown crust. The internal temperature should reach 165°F. Transfer chicken to a plate and tent with foil to keep warm.

Reduce heat to medium and add the remaining tablespoon of olive oil to the same pan (don't wipe it out, those browned bits add flavor). Add minced garlic and 2 teaspoons Italian seasoning, stirring constantly for about 30 seconds until fragrant but not browned.

Pour in the lemon zest, lemon juice, and heavy cream. Season with a pinch of salt and pepper, then let the sauce simmer gently for 2-3 minutes until it thickens enough to coat the back of a spoon. Stir in the shaved Parmesan cheese until completely melted and the sauce looks glossy and smooth.

Add the cooked spaghetti to the sauce and toss with tongs to coat every strand evenly. If the sauce seems too thick, add reserved pasta water a splash at a time until you reach a silky consistency. Slice the chicken into strips and nestle it into the pasta. Toss everything together until heated through, about 1-2 minutes.

Taste and adjust seasoning with additional salt and pepper if needed. Serve immediately topped with fresh parsley and lemon wedges on the side.