Make the rub for the chicken thighs by combining whole-grain mustard, 1 teaspoon of zest, oregano, basil, and 1 tablespoon of olive oil in a small bowl.
Coat each side of the chicken with the mustard rub, and season both sides with sea salt and freshly cracked pepper to taste.
Whisk the remaining lemon zest (2 teaspoons), lemon juice, and the chicken broth in a measuring cup. Set aside.
Heat the remaining tablespoon of oil in a Dutch oven or a large OVENPROOF skillet over medium heat. Add the chicken to the hot oil and cook for 2 to 3 minutes or until golden brown.
Flip the chicken, add the minced garlic to the pan, and cook, stirring constantly, for 30 seconds.
Add the lemon mixture and stir, scraping any browned bits from the bottom of the pan.
Place the pan in the oven and bake for 20 minutes, or until the chicken is cooked.
Remove the Dutch oven from the oven, transfer the chicken to a plate, and cover it with a foil tent.
Place the Dutch oven over medium heat and bring the liquid to a gentle boil.
Use your fingers to mix the butter and flour, creating a dry, crumbly paste.
Whisk the flour and butter into the sauce. The sauce will thicken slightly and look glossy. Taste and season with sea salt and freshly cracked pepper, if needed.
Return the chicken and its juices to the Dutch oven, and coat it with the sauce.