How to Make It
Preheat the oven to 450°. In a medium skillet, combine the orange juice with 1/4 cup of the olive oil, the orange zest, cumin seeds, garlic and a generous pinch of salt and simmer over moderate heat for 3 minutes. Reduce the heat to low and add the carrots, then cover and cook until the carrots are very tender but still hold their shape, about 45 minutes. Transfer the carrots to a plate and keep warm. Increase the heat to high and simmer the sauce until reduced to a syrupy glaze, about 3 minutes. Remove the skillet from the heat and stir the lemon juice and 1 tablespoon of olive oil into the orange sauce.
Stand the lemon halves on their ends in a small ovenproof dish. Sprinkle each lemon half with 1 teaspoon of sugar and bake for about 20 minutes, or until the sugar is melted and the lemon pulp is soft. Remove the dish from the oven and cover the lemons with foil to keep them warm. Increase the oven temperature to 500°.
Season the snapper fillets with salt and pepper. Heat the remaining 3 tablespoons of olive oil in a large nonstick ovenproof skillet. Add the snapper fillets, skin side down, and cook over high heat until browned on the bottom, about 2 minutes. Transfer the skillet to the oven and roast the fillets for 6 to 8 minutes, or until they are opaque. Arrange the snapper fillets, skin side up, on plates with the carrots alongside. Drizzle the orange sauce on the fish and garnish with the coarsely chopped cilantro and baked lemon halves.