Season the chicken breast evenly with half of the sea salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat and sear the chicken for 6-7 minutes per side until the internal temperature reaches 165°F.
Remove the chicken from the pan and set it aside on a plate to rest, keeping the juices in the pan.
Add the ghee to the same skillet, followed by the sliced cremini mushrooms, sautéing until they release their moisture and turn a deep umami brown.
Stir in the minced garlic and fresh thyme, cooking for 1 minute until the aromatics are fragrant.
Pour in the balsamic vinegar to deglaze the pan, scraping up any browned bits from the bottom, and toss the mushrooms to coat thoroughly.
While the mushrooms finish, steam the green beans for 4-5 minutes until tender-crisp and season with the remaining salt and pepper.
Plate the chicken breast, topping it generously with the sautéed mushrooms and balsamic reduction, and serve alongside the green beans.