Slash the chicken thighs by placing on a cutting board with skin facing up. 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 (but not all the way through to the other side).
In a large bowl, combine Dash™ Garlic & Herb Seasoning, garlic, 3 tablespoons vinegar, 1 tablespoon mustard, and 1¾ teaspoons salt. Add chicken and toss; press the marinade into the slashes. Let marinate at room temperature while the grills heats up, or cover and marinate in the refrigerator overnight.
Remove the chicken from the fridge to come to room temperature if needed. Heat the grill to medium.
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.
Once 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 is easy to remove from the grates, about 3 minutes, then uncover. Rotate the chicken 45 degrees without flipping, and grill for 3 to 4 more minutes.
Flip the chicken and add the tomatoes to the grill, cut sides down. Close the lid again and grill the second side of the chicken and the tomatoes until the chicken is cooked through and the tomatoes are charred and soft, 7 to 9 minutes - the internal temperature should reach 165℉.
On a serving platter, spread about a tablespoon of the mustard vinaigrette on the plate. Place the chicken and tomatoes on top of the mustard vinaigrette. Spoon the remaining vinaigrette onto the tomatoes. Let everything rest for 5 to 10 minutes, then top with arugula (if desired) and drizzle with olive oil.