Place a rack in top third of oven; preheat to 375°F. Whisk Dijon mustard, 2 Tbs honey, and 1 Tbs oil in a medium bowl to combine. Season chicken on all sides with 1 tsp salt and 1/2 tsp pepper. Transfer to bowl with honey mustard and toss to coat.
Toss potatoes, 2 Tbs oil, 1 tsp salt, and remaining 1/2 tsp pepper on a rimmed baking sheet. Arrange drumsticks (skin side up) in the center of pan; discard excess marinade.
Arrange potatoes around outside of pan in an even layer, then turn cut side down . Arrange thyme over potatoes. Roast until chicken and potatoes are golden brown and an instant-read thermometer inserted into thickest part of chicken registers 165F/85C, 30–40 minutes.
Whisk garlic, lemon juice, whole grain mustard, and remaining 1/3 cup oil, 2 tsp honey, and 1/2 tsp salt in a small bowl. Divide chicken and potatoes among plates. Drizzle dressing over chicken, and potatoes