Preheat the oven to 425°F. Lightly grease a large rimmed sheet pan or line it with parchment paper.
Add the halved baby potatoes to the sheet pan. Drizzle with about 1 tablespoon olive oil and season with salt, pepper, garlic powder, paprika and oregano. Toss until evenly coated and arrange the potatoes cut-side down when possible.
Roast the potatoes for 10 minutes to give them a head start.
While the potatoes roast, make the lemon Dijon sauce. Whisk together the Dijon mustard, lemon juice, honey, garlic, olive oil, salt, pepper and thyme or rosemary until smooth.
Pat the chicken thighs dry with paper towels. This helps the skin get nice and golden.
Remove the sheet pan from the oven. Toss the potatoes and add the chicken thighs, skin-side up, along with the broccoli or green beans. Drizzle the vegetables lightly with the remaining olive oil and season with a pinch of salt and pepper.
Generously brush or spoon the lemon Dijon sauce over the chicken thighs. Add a few lemon slices around the pan, if desired.
Return the pan to the oven and roast for another 20–25 minutes, or until the chicken is cooked through and reaches at least 165°F internally and the potatoes are tender and golden.
For extra crispy chicken skin, broil for 2–3 minutes at the end.
Finish with fresh parsley and an extra squeeze of fresh lemon before serving.