Pat chicken completely dry with paper towels. This is crucial for a good sear. Season both sides evenly with salt and pepper. Let sit at room temperature while you prep the remaining ingredients.

Heat 1 tablespoon olive oil in a large skillet over medium-high heat until shimmering. Add chicken in a single layer, working in batches if needed to avoid crowding. Cook undisturbed until deeply golden brown on the first side, about 5-6 minutes. Flip and cook 3-4 minutes more until just cooked through (165 degrees F for breasts, 175 degrees F for thighs). Transfer to a plate.

Reduce heat to medium. Add remaining 1 tablespoon olive oil to the same skillet. Add garlic and red pepper flakes if using. Cook 30-60 seconds until fragrant and just starting to turn golden at the edges - do not let it brown or it will turn bitter.

Add crushed tomatoes with their juices, scraping up any browned bits from the pan bottom. Stir in balsamic vinegar. Bring to a lively simmer, then reduce heat to maintain a gentle bubble. Cook 10-12 minutes, stirring occasionally, until sauce has thickened slightly and lost its raw tomato edge. Taste and adjust salt as needed.

Nestle chicken and any accumulated juices back into the skillet. Simmer 2-3 minutes to rewarm and let flavors meld. Remove from heat, scatter torn basil over top, and let rest 5 minutes. Serve directly from the skillet, passing Parmesan at the table if desired.