Pat the chicken thighs dry with paper towels. Season both sides with kosher salt and black pepper.
Heat the olive oil in a large skillet over medium-high heat until shimmering.
Place the chicken thighs skin-side down in the skillet. Cook without moving for 7 to 8 minutes, until the skin is golden brown and crispy.
Flip the chicken thighs and cook for an additional 7 minutes on the other side, until browned and cooked through. Remove the chicken from the skillet and set aside on a plate.
Reduce the heat to medium. Add the minced garlic to the skillet and sauté for 30 seconds until fragrant, stirring constantly to avoid burning.
Add the Dijon mustard, chicken broth, lemon juice, and dried thyme to the skillet. Stir well to combine and scrape up any browned bits from the bottom of the pan.
Simmer the sauce for 2 to 3 minutes until slightly thickened.
Return the chicken thighs to the skillet, spooning some sauce over them. Cook for an additional 2 minutes to heat through.
Remove the skillet from heat. Stir in the unsalted butter until melted and the sauce is glossy.
Sprinkle the chopped fresh parsley over the chicken and sauce before serving.