Preheat the oven to 425°F (220°C).
In a bowl, whisk together the balsamic vinegar, honey, Dijon mustard, 1 tablespoon of the olive oil, minced garlic, and Italian seasoning until smooth.
Pat the chicken breasts dry with paper towels and season both sides with salt and freshly ground black pepper.
Place the chicken in the bowl or a shallow dish with the marinade and turn to coat; let sit for at least 10 minutes.
Heat an oven-safe skillet over medium-high heat and add the remaining 1 tablespoon olive oil. When the oil is hot, sear the chicken 3 minutes per side until golden brown.
Pour any leftover marinade over the seared chicken, then transfer the skillet to the preheated oven.
Bake 13–17 minutes, or until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Remove the skillet from the oven and let the chicken rest 5 minutes, then garnish with chopped fresh parsley and serve.