Preheat oven to 200c. Combine salt, pepper, coriander, cumin, and paprika in a small bowl. Rub carrots with spice mixture, reserving 3/4 tsp. in bowl.

Heat oil in a large ovenproof heavy fry pan or griddle (preferably cast-iron) over medium-high until shimmering. Add carrots cut side down and sear until crisp and browned, 5–6 minutes. Flip carrots and transfer to oven. Roast carrots until tender when pierced with a knife and nicely browned on the outside, 20–25 minutes. Transfer pan back to stovetop over medium heat. Add butter and reserved spice mixture, and once melted, use a spoon to baste carrots with spiced butter for about 3 minutes.

Transfer carrots to a serving platter or divide among plates. Drizzle with remaining spiced butter from skillet and squeeze lemon over. Sprinkle with parsley and sea salt.