Pat the chicken breasts dry with paper towels. Season both sides with kosher salt and black pepper.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat until hot but not smoking.
Add the chicken breasts to the skillet and cook for 5-6 minutes on each side, until golden brown and cooked through (internal temperature should reach 165°F). Remove chicken from the skillet and set aside on a plate.
Reduce heat to medium. Add the remaining 2 tablespoons of butter to the skillet. Once melted, add the minced garlic and sauté for 30 seconds until fragrant.
Stir in the Dijon mustard, fresh lemon juice, and chicken broth. Scrape the bottom of the skillet to loosen any browned bits. Simmer the sauce for 3-4 minutes until slightly thickened.
Return the chicken breasts to the skillet, spooning the sauce over them. Cook for an additional 2 minutes to heat through and allow flavors to meld.
Sprinkle chopped fresh thyme over the chicken and sauce. Serve immediately.