Preheat outdoor grill to medium heat or set stove to high heat and preheat indoor grill pan.
Pat the chicken dry with paper towels, evenly drizzle with olive oil as desired, and evenly sprinkle the Italian seasoning, garlic powder, salt, and pepper over the chicken on both sides.
Place the chicken on either your outdoor grill or indoor grill pan and cook for about 3 minutes per side, or as needed, until the chicken is nearly done.
In the final 1 minute of cooking, place the cheese slices over each piece of chicken.
If you want to grill your tomatoes, do it now while the cheese is melting. Lightly drizzle the tomatoes with a bit of olive oil, add a pinch of salt and pepper to them, and then grill them for about 60-90 seconds per side, or as desired.
Top the melted cheesy layer on each piece of chicken with the tomatoes and evenly sprinkle with basil ribbons.
As desired, evenly drizzle with balsamic glaze.
Optionally for serving, drizzle with olive oil, and add flakey sea salt or pepper, as desired, and serve warm and fresh.
