Preheat the oven to 425°F (220°C). Lightly grease a rimmed baking sheet or a 9x13 baking dish and set aside.
Combine the dry seasoning ingredients in a large bowl: salt, black pepper, dried Italian herbs, dry mustard, smoked paprika, brown sugar, onion powder, and garlic powder.
Pat the chicken thighs dry with paper towels, then rub them with 2 tablespoons olive oil to coat evenly.
Add the oiled chicken thighs to the bowl with the seasoning and toss to coat each piece generously and evenly.
Arrange the seasoned chicken thighs skin-side up on the prepared baking sheet or dish, spacing them so air can circulate.
Bake in the preheated oven for 35–40 minutes, until the skin is golden and the internal temperature reaches 165°F (74°C).
If desired, switch the oven to broil and broil for 2–3 minutes to crisp the skin further—watch closely to avoid burning.
While the chicken bakes, make the sauce: in a medium bowl whisk together 2 tablespoons olive oil, whole-grain Dijon, yellow mustard, mayonnaise, honey, and minced garlic until smooth.
Serve the baked chicken thighs with the honey-mustard garlic sauce on the side and garnish with chopped parsley if desired.