Bring a large pot of salted water to a boil and cook spaghetti until al dente, about 8 to 9 minutes. Before draining, scoop out 1/2 cup of pasta water and set aside. Drain pasta, toss with 1 tablespoon olive oil, and set aside.

While pasta cooks, slice each chicken breast in half lengthwise to create cutlets about 1/2-inch thick. In a shallow bowl, combine flour, 1 teaspoon Italian seasoning, lemon pepper seasoning, salt, and pepper. Dredge each chicken piece in the flour mixture and shake off excess.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add the coated chicken and cook 4 to 5 minutes per side until deeply golden brown and cooked through (internal temp 165 degrees F). Do not move the chicken while it cooks. Remove to a plate and set aside.

Reduce heat to medium and add the remaining tablespoon of olive oil to the same pan. Add minced garlic, remaining teaspoon Italian seasoning, salt, and pepper. Stir constantly for about 30 seconds until fragrant but not browned.

Add lemon zest, lemon juice, and heavy cream to the pan. Stir well and season with salt and pepper. Let the sauce warm through and thicken slightly, about 2 to 3 minutes, until it coats the back of a spoon. Stir in Parmesan cheese until melted and smooth.

Add the cooked spaghetti and toss to coat, adding reserved pasta water 2 tablespoons at a time until you reach your desired consistency. Slice the cooked chicken into strips and return to the pan, stirring until heated through. Taste and adjust seasoning as needed.

Serve immediately, garnished with fresh chopped parsley and lemon wedges on the side.