Start by mixing balsamic vinegar, pesto, honey, red pepper flakes, salt, and pepper in a bowl until well-blended and smelling tangy. Place the chicken in a resealable bag and pour the marinade over it. Let it soak in the marinade for at least 1 hour.
Boil a pot of salted water and add your uncooked pasta, stirring occasionally. Cook until al dente, which will take about 8 to 10 minutes. Reserve 1 cup (240 milliliters) of pasta water before draining the pasta and then drain it.
Heat olive oil in a grill pan over medium heat. Add the marinated chicken to the pan. Cook for about 6 to 7 minutes on each side, or until the chicken is golden brown and no longer pink inside. Make sure not to overcook to avoid dryness.
In the same pan used for grilling chicken, add minced garlic. Cook for about 1 minute until fragrant. Then add the halved cherry tomatoes and a pinch of red pepper flakes. Stir until the tomatoes soften and burst, about 2 to 3 minutes.
Mix in the drained pasta and toss it with the garlic-tomato blend. If the pasta seems dry, slowly pour in reserved pasta water until the desired consistency is reached. Keep the heat low to prevent sticking.
Add chopped fresh basil and gently mix, allowing the heat to bring out the aroma. Avoid cooking the basil too long; it should remain vibrant.
Plate the pasta and top with shredded Parmesan cheese. Drizzle with balsamic glaze and sprinkle extra basil if desired before serving.