Season the chicken cutlets with salt and pepper. In a large skillet, heat olive oil over medium-high heat and sear the chicken until golden brown and cooked through, about 3-4 minutes per side. Remove to a plate and set aside.
In the same skillet, add minced garlic and sauté for about 30 seconds until fragrant. Add halved cherry tomatoes and cook until they start to soften and release their juices, about 4-5 minutes.
Pour in the heavy cream and chicken broth, stirring to combine. Add honey, lemon juice, oregano, and parmesan cheese. Let the sauce simmer gently until it thickens slightly, about 4-6 minutes.
Return the chicken to the pan and nestle it into the sauce. Let everything simmer together for 2-3 minutes to meld flavors and reheat the chicken. Taste and adjust seasoning with salt and pepper as needed.
Meanwhile, cook the pasta in salted water according to package directions until al dente. Reserve a splash of pasta water, then drain.
If the sauce seems too thick, loosen it with a splash of pasta water. Toss the cooked pasta with the sauce until well coated. Add torn basil leaves and give a gentle stir.
Serve immediately, garnishing with extra parmesan and a few basil leaves for a fresh, fragrant finish.