Begin by slashing the chicken thighs: Hold each thigh down on a cutting board with skin facing up and pierce the skin with a knife, then drag the knife perpendicular to the bone to make a deep cut. Repeat on each thigh to make two slashes through the skin and flesh to the bone.

In a large bowl or container, combine the herbes de Provence, garlic, 3 tablespoons vinegar, 1 tablespoon mustard and 1¾ teaspoons salt. Add chicken and toss and squelch the marinade into the slashes. Let marinate at room temperature while the grills heats up or, ideally, cover and marinate in the refrigerator overnight.

When ready to cook, remove the chicken from the fridge to come to room temperature if needed. Light the grill to medium.

Meanwhile, in a small bowl, mix the olive oil with the remaining 1 tablespoon vinegar, 1 tablespoon mustard and ¼ teaspoon salt. Stir vigorously until the ingredients come together into a thick vinaigrette. Set aside.

When the grill is hot, place the chicken on the grill skin side down and close the lid. Grill until the skin has dark brown char lines and releases easily from the grates, about 3 minutes, then uncover. If there are any flare ups, remove the chicken from the grate and let the flames die, then wipe off any fat on the grate with tongs gripping a dish towel. Rotate the chicken 45 degrees without flipping, and allow the chicken skin to color for 3 to 4 more minutes.