Preheat oven to 425°F for exactly 15 minutes while you prep ingredients and pat thighs completely dry with paper towels. Moisture is the enemy of crispy skin—this critical step cannot be rushed or skipped under any circumstance.
Combine garlic powder, paprika, onion powder, thyme, rosemary, salt, pepper, and cayenne in a small bowl. Rub olive oil directly onto each thigh's skin, then coat generously with the spice mixture, paying special attention to edges where seasoning adheres best and renders golden.
Arrange baby potatoes and green beans in a single layer on a large sheet pan, drizzle with 1 tablespoon olive oil, and season with salt and pepper. Place thighs skin-side up directly on the vegetables—this setup creates the elegant one-pan dinner you need.
Roast at 425°F for 35 minutes until skin turns deep golden brown and internal temperature reaches 165°F at the thickest part without touching bone. The stunning chicken thighs should have rendered fat pooling beneath crispy skin while vegetables caramelize underneath.
Remove the pan from the oven and transfer thighs to a warm plate; set vegetables aside. Pour off all but 2 tablespoons of pan drippings, place the sheet pan over medium heat, and add minced garlic and butter, stirring constantly for 60 seconds until fragrant.
Add lemon juice, chicken broth, and Dijon mustard to the hot pan, scraping browned bits from the surface with a wooden spoon—this deglazing step recovers all the caramelized flavor from your crispy baked chicken thighs elegant preparation. Simmer for 2 minutes until sauce reduces slightly.
Return thighs to the pan alongside vegetables, turn to coat with sauce, and serve immediately while skin remains crispy and meat is at peak temperature.