Heat the oven to 425°F and line a large rimmed sheet pan with parchment or foil.

Whisk the Dijon mustard, honey, olive oil, garlic, lemon juice or apple-cider vinegar, half the kosher salt, black pepper, and optional smoked paprika or dried thyme in a bowl. Set aside one-third of the sauce for serving.

Toss the halved potatoes with a little additional olive oil and the remaining kosher salt. Arrange them cut-side down on the prepared pan and roast for 10 minutes.

Coat the chicken with about two-thirds of the remaining honey-mustard sauce. Add the chicken and green beans or broccoli to the pan, leaving space between the ingredients.

Roast for another 15 to 20 minutes, turning the vegetables once, until the potatoes are tender and the chicken reaches 165°F in the thickest part.

Rest the chicken briefly, then serve it with the roasted potatoes, vegetables, and reserved sauce. Never reuse sauce that touched raw chicken unless it has been boiled first.