Pat chicken pieces dry with paper towels and season generously with salt and pepper on both sides. This moisture removal ensures golden browning rather than steaming. Let sit at room temperature for five minutes before cooking.
Heat olive oil in a large skillet over medium-high heat until shimmering, approximately two minutes. Add chicken pieces in a single layer without crowding the pan—work in batches if necessary. Sear for 5-6 minutes per side until golden brown, then transfer to a plate temporarily.
Reduce heat to medium and add minced garlic to the same skillet, stirring constantly for 30 seconds until fragrant. Don't allow the garlic to brown; it should smell wonderful but remain light golden. Add the chicken broth next, scraping up any browned bits from the bottom.
Whisk together balsamic vinegar, honey, Dijon mustard, Italian seasoning, and red pepper flakes in a small bowl before adding to the skillet. Return chicken pieces to the pan, nestling them into the glaze. Balsamic glazed chicken cooks through as the sauce reduces around it, approximately 12-15 minutes at a gentle simmer.
The glaze should coat the back of a spoon and cling to the chicken pieces when ready. Stir in butter and fresh basil during the final minute, allowing them to incorporate into the sauce. Taste and adjust seasoning with additional salt or pepper as needed before plating.