Season the chicken breast evenly on both sides with the sea salt, black pepper, and dried thyme.
Heat the olive oil in a medium skillet over medium-high heat until shimmering.
Place the chicken in the skillet and sear for 6 to 7 minutes per side until golden brown and the internal temperature reaches 165°F.
Remove the chicken from the pan and let it rest on a plate; meanwhile, steam the broccoli florets in a separate pot until tender-crisp.
In the same skillet used for the chicken, add the ghee and minced garlic, sautéing for 30 seconds until fragrant.
Whisk the arrowroot powder into the cold chicken broth until completely dissolved, then pour the mixture into the skillet.
Simmer the sauce for 2 to 3 minutes, whisking constantly to scrape up any browned bits, until it thickens into a silky gravy.
Slice the chicken, plate it alongside the steamed broccoli, and pour the warm gravy over the top.