Pat the chicken thighs dry and season both sides with the salt, pepper, and rosemary. Slice the mushrooms and mince the garlic.

Heat the olive oil in a large skillet over medium-high heat. Sear the chicken, smooth side down, for 6 minutes without moving it, then flip and cook 5 to 6 minutes more, until it reaches 175°F. Move to a plate.

Add the mushrooms to the same skillet and cook 5 minutes, stirring only once or twice, until browned. Add the garlic and stir for 30 seconds.

Pour in the balsamic vinegar and chicken broth and scrape up the browned bits. Whisk in the dijon and simmer 3 to 4 minutes, until reduced by about half.

Remove the pan from the heat and swirl in the butter until the sauce turns glossy.

Return the pan to low heat, add the spinach, and stir until just wilted, about 1 minute.

Nestle the chicken and any juices back into the skillet and spoon the sauce over the top. Serve right away.