In a large, deep skillet with a lid, heat the olive oil to medium-high heat. As it heats, mince the garlic cloves and dice the onion. If you want to chop your sun-dried tomatoes into smaller pieces, you can do so, though we left ours whole.
Season chicken well with salt and pepper. When skillet is heated, add the chicken thighs. Cook each side for 8-10 minutes, or until the chicken is cooked through with no pink left.
As the chicken thighs cook in the skillet, whisk together the balsamic vinegar, yellow mustard, and honey in a small bowl.
When the chicken is cooked through, add the onions to the skillet. Sauté for about 2 minutes, until translucent. Add the garlic and cook through for 1 minute, until fragrant.
Add the balsamic mixture to the pan, stirring constantly with a whisk or wooden spoon to scrape up the brown bits from the bottom. This is your deglazing step, so be sure to get those crusty, flavorful bits. Simmer for 3 minutes, stirring constantly.
Reduce heat to medium-low. Add the sun-dried tomatoes and basil to the pan with the onions and garlic. Cook for about 2 minutes.
Evenly spread the mozzarella cheese on each chicken thigh. Place lid on the skillet and cook for five minutes more, or until the mozzarella is fully melted. Voila!