Prep and season the chicken: Pat the drumsticks very dry with paper towels — dry skin crisps better in the oven. In a large bowl, toss the drumsticks with 1 tsp kosher salt, 1/2 tsp black pepper, smoked paprika and 1 tsp chopped thyme. Let rest at room temperature for 15–20 minutes while you prepare the potatoes; this short sit helps the seasoning penetrate and takes the chill off so they roast evenly.

Parboil the potatoes for crisp edges: Place the cut potatoes in a pot of cold salted water, bring to a simmer and cook for 8 minutes — not fully cooked. Parboiling softens the interior and loosens the exterior so the edges roughen when shaken; those rough edges create more surface area for browning in the oven. Drain well and let steam-dry in the colander for 2–3 minutes.

Roughen the potato surface: Return the drained potatoes to the empty pot, cover and give the pot a couple of good shakes for 20–30 seconds to roughen the surfaces — this encourages crunchy, golden crusts when roasted.

Preheat the oven to 220°C / 425°F and arrange a large roasting pan or rimmed baking sheet with a wire rack (if you have one). A hot oven and a rack allow air to circulate and crisp the chicken skin while roasting; the higher temperature promotes Maillard browning.

Toss potatoes with oil and aromatics: In a bowl, combine the parboiled potatoes with 1 tbsp olive oil, 1/2 tsp kosher salt, 1/4 tsp pepper and 1 tsp chopped rosemary (or thyme). Spread them in an even layer on the baking sheet; overcrowding will steam, not roast, so give them space.

Start roasting potatoes and sear the chicken: Put potatoes in the oven and roast for 10 minutes. Meanwhile, heat a large skillet over medium-high heat with 1 tbsp olive oil. Sear the drumsticks, skin side down first, for 3–4 minutes until deeply golden — searing starts the browning process and renders some fat from the skin for extra flavor. Flip briefly, then transfer chicken to the rack over the potatoes (or beside them) skin side up.

Make herb-garlic butter for basting: In a small saucepan or microwave, melt 4 tbsp (56 g) butter with the minced garlic, lemon zest and the remaining chopped thyme. Warm butter melds garlic and herb flavors; you'll baste with this to build glossy, aromatic skin.

Roast together and baste: Put the baking sheet with potatoes and chicken into the hot oven. Roast for 20–25 minutes, then baste the drumsticks with the garlic-herb butter (use a brush or spoon) — basting at this stage adds layers of flavor and promotes even browning. Roast another 8–12 minutes until the chicken reaches an internal temperature of 74°C / 165°F at the thickest part and the potatoes are golden and crisp.

Cook the mixed vegetables and soft-boil eggs: While the chicken roasts, heat a sauté pan over medium heat with the remaining 1 tbsp butter. Add the chopped onion and sweat gently until translucent (2–3 minutes) to sweeten and build flavor, then add minced garlic and cook 30 seconds to bloom. Add the mixed vegetables and toss until heated through and just tender (4–6 minutes for frozen), season with 1/2 tsp salt, a pinch of pepper and 1 tbsp lemon juice to brighten. For the eggs: bring a small pot of water to a vigorous simmer, add eggs and cook for 6 minutes for jammy yolks; immediately transfer to an ice bath for 3 minutes before peeling and halving.

Rest and finish: Remove the chicken from the oven and let rest 5 minutes — resting redistributes juices and avoids a flood of hot juices when you cut. Give the potatoes a final sprinkle of flaky sea salt and toss the vegetables with chopped parsley and the remaining 2 tbsp butter for a glossy finish.

Plate: Spoon sautéed mixed vegetables onto plates, place 2 drumsticks per person, add a generous scoop of crispy potatoes, top the vegetables with a halved jammy egg and spoon a little of the pan juices or extra melted butter over the chicken. Garnish with lemon zest and parsley for brightness.

Why these steps: The combined techniques — parboiling and roughening potatoes, searing then roasting chicken at high heat, and basting with herb-butter — maximize Maillard reaction (browning) and flavor while keeping meat moist. The jammy egg and buttered veg add richness and textural contrast that make the dish feel restaurant-quality.