Cook the Pasta: Bring a large pot of heavily salted water to a boil. Add the pasta and cook according to package directions until al dente. Drain (don’t rinse) and set aside.
Season & Cook the Chicken: While the pasta cooks, slice each chicken breast in half lengthwise so you have 4 thinner cutlets. Pat dry, then season both sides with the Italian seasoning, granulated garlic, ¼ teaspoon of the salt, and black pepper.
Heat 1 tablespoon of the olive oil in a large skillet over medium-high heat. Add the chicken and cook for 5-6 minutes per side until golden and cooked through (165°F internal temp). Transfer to a cutting board and let rest for 5 minutes, then slice into strips.
Cook the Vegetables: Turn the same skillet (no need to wash it first) to medium heat. Add the butter butter, 1 tablespoon of olive oil, and the minced garlic. Cook for 1 minute, stirring constantly. Add the asparagus, cherry tomatoes, and ¼ teaspoon of salt.
Cook for 3 to 4 minutes, stirring occasionally, until the asparagus is just tender and bright green and the tomatoes begin to soften and release their juices (a few will burst slightly, which is exactly what you want).
Make the Sauce: Reduce the heat to medium-low and add the chicken stock and ¼ teaspoon of salt. Simmer for 2-3 minutes to reduce slightly. Turn off the heat and add the lemon juice, lemon zest, and heavy cream, stirring to combine. Add the pasta back to the pan, tossing to coat in the sauce. Add the Parmesan and toss until well combined.
Serve: Divide among bowls and top with the sliced chicken, freshly grated Parmesan and basil if that’s your thing.