Prep the chicken: Pat the chicken breasts dry. If they’re very thick, slice horizontally to create cutlets or pound to even thickness (about 3/4 inch). Season both sides with salt, pepper, garlic powder, and Italian seasoning.
Heat the pan: Set a large skillet over medium-high heat.
Add 1 tablespoon olive oil. When it shimmers, add the butter if using.
Sear the chicken: Place chicken in the pan without crowding. Sear 4–6 minutes per side, until golden with an internal temperature of 160°F.
Adjust heat to prevent burning.
Top with Caprese: Lower heat to medium-low. Place 2 slices of tomato on each breast, then 2 slices of mozzarella. Cover the pan for 1–2 minutes until the cheese softens but doesn’t fully melt into a puddle.
Rest and move: Transfer chicken to a plate and tent loosely with foil to rest.
Keep the pan on the stove for the sauce.
Make a quick pan sauce: Add remaining 1 tablespoon olive oil to the skillet. Pour in the balsamic vinegar, add Dijon, and whisk, scraping up brown bits. Simmer 1–2 minutes.
Taste and add a pinch of sweetener if you want a smoother, less tangy finish. Season with salt and pepper.
Finish with basil: Spoon a little sauce over each chicken breast. Scatter fresh basil over the top.
Sprinkle with flaky sea salt if you like a little crunch.
Serve: Plate with a side of sautéed zucchini, garlicky spinach, or a simple arugula salad to keep things low-carb and balanced.