Step 1: Preheat and Prep Vegetables: Preheat your oven to 425°F (220°C). On a large rimmed baking sheet, combine the broccoli florets, carrot chunks, potato chunks, and onion wedges. Drizzle with 2 tablespoons of olive oil and sprinkle with ½ teaspoon salt and ¼ teaspoon black pepper. Toss everything with your hands until every piece is coated. Spread the vegetables into an even layer, leaving gaps where the chicken thighs will go. Do not crowd the pan — ingredients need at least a finger's width of space between them for air to circulate. Overcrowding traps steam and turns roasting into steaming.
Step 2: Season the Chicken: In a small bowl, mix the remaining 1 tablespoon of olive oil, garlic powder, rosemary, thyme, smoked paprika, remaining ½ teaspoon salt, and remaining ¼ teaspoon black pepper into a paste. Place the chicken thighs skin-side up in the gaps on the baking sheet. Using your fingers, spread the herb paste evenly over the skin of each thigh — make sure every piece of skin is coated. Skin-side up is critical: this positions the fat directly above the vegetables, so as it renders, it drips down and bastes everything on the pan.
Step 3: Roast for 20 Minutes: Place the pan on the middle rack of the preheated oven and roast for 20 minutes. During this time, the chicken skin will begin to render and turn golden, while the bottom edges of the vegetables — especially the potatoes touching the hot metal — will start to brown and crisp.
Step 4: Toss Vegetables and Continue Roasting: Pull the pan from the oven. Using tongs or a spatula, toss the vegetables — this flips them so the sides that were touching the pan get a turn facing up, and the sides that were facing up make contact with the hot metal. Do not flip the chicken; the skin stays up the entire time. Return the pan to the oven and roast for another 15 minutes, for a total of 35 minutes. If you want extra-crispy chicken skin, switch the oven to broil for the last 2 minutes — but watch it closely.
Step 5: Finish and Serve: Remove the pan from the oven. Squeeze the lemon halves over the chicken and vegetables — the juice will sizzle on contact with the hot pan. Let everything rest for 5 minutes before serving. The chicken skin should be golden and crackling-crisp, the vegetable edges should show visible caramelization, and the potatoes should be tender inside with a lightly crisped exterior. Spoon any juices and rendered fat from the pan over the vegetables — that's concentrated flavor you don't want to leave behind.