Preheat oven to 400 degrees F. Peel carrots, and cut into coins.: The oven should be hot enough so the carrots roast and develop caramelized edges rather than steam. As it comes up to temperature you may smell the faint warmth of the heating element, and once the oven is ready the air inside feels noticeably warmer. A common mistake is putting vegetables into an oven that is not fully preheated, which can lead to uneven color and a limp texture.
Melt butter and pour into a small mixing bowl. Add honey, sugar, salt, cinnamon and nutmeg. Whisk to combine.: Slicing into uniform coins ensures consistent cooking and a pleasing mouthfeel. When you cut, listen for the clean snap of a crisp carrot , and look for rounds of similar thickness, about a quarter inch to a half inch, so they finish at the same time. If slices vary widely, thinner pieces will overcook while thicker ones remain firm, so take a few extra moments to match sizes.
Place carrots onto a baking sheet and drizzle with all but 1 tablespoon of glaze. Toss carrots to more evenly coat.: As the butter melts it should go from opaque to glossy liquid, releasing a gentle, nutty aroma. Pour it into a bowl so you can whisk it easily with the sweeteners and spices. If the butter browns, stop heating immediately to avoid a burnt flavor; brown butter is tasty in some recipes, but here you want pure richness to carry the glaze.
Roast in oven for 15-20 minutes. Drizzle with reserved glaze and serve.: When you add the honey and brown sugar to the melted butter , you will feel the mixture thicken slightly as the sugar dissolves. The aroma will shift toward warm spice from the cinnamon and a subtle savory lift from the salt. Whisk until smooth and glossy so the glaze is homogeneous; if the sugar has not fully dissolved you may notice tiny grains, which can create uneven texture on the finished surface.
Whisk to combine: A good whisking yields a cohesive, syrupy glaze that clings to a spoon. Visually it should be smooth and slightly viscous. If the glaze separates, whisk again and a little warm butter can help bring it back together. Avoid overheating, which can thin the glaze and make it run off the carrots instead of coating them.
Place carrots onto a baking sheet and drizzle with all but 1 tablespoon of glaze: Spread the carrots in a single layer so each piece has contact with the hot sheet, which encourages browning. Drizzle most of the glaze over them, but reserve one tablespoon for finishing so the surface stays shiny after roasting. You should hear a faint sizzle if the sheet is warm, and visually the glaze should make the carrots gleam. Crowding the pan is a common error, it steams vegetables instead of roasting them.
Toss carrots to more evenly coat: Use tongs or a spatula to gently turn the rounds so every side gets glaze. You want a thin, even coating rather than clumps. When tossed correctly the carrots will look uniformly glossy, which helps them caramelize consistently in the oven. Over tossing can break fragile pieces, so be gentle.
Roast in oven for 15 to 20 minutes: While roasting you will notice the sweet smell intensify, and the edges of the carrots should take on a golden to deep amber hue. The texture should change from firm to tender with a slight give when pierced. Check at the earlier time point to avoid overcooking; a common mistake is leaving them too long which yields a mushy interior. Rotate the pan halfway through if your oven has hot spots to ensure even color.
Drizzle with reserved glaze and serve: After the carrots come out of the oven, the heat will be enough to slightly loosen the glaze so it spreads beautifully. Drizzling the reserved tablespoon at the end brings bright shine and a fresh burst of flavor. The surface should glisten and the aroma of warmed honey and spice will be vivid. Avoid pouring too much extra glaze or the dish can become sticky and overly sweet, a light finish is all you need.