Why? Cranking up the oven temperature caramelizes the vegetables' outer layer. If too high, the interior won't fully cook; if too low, the vegetables won't brown well. Roasting temperatures will range between 375° for larger items and 450° for smaller items.
Scrub carrots, and dry well; peel, if desired. Why? The goal is a dry roasting environment. Excess moisture can make outer surfaces mushy and inhibit browning. Peeling is a matter of choice: Some peels taste bitter.
Arrange carrots in a single layer, well spaced on a baking sheet. Why? Roast similar types and sizes of vegetables together so everything cooks at the same rate. To encourage caramelization, make sure each vegetable sits directly on the sheet pan, and allow room for heat to circulate.
Drizzle with oil, turning to coat all over. Sprinkle with salt and pepper.
Why? A light coating of oil promotes browning and prevents sticking. But go easy: Too much oil will just soak into porous vegetables, or pool and "fry" nonporous ones. Avoid using butter, which can burn.
Tightly cover pan with foil. Bake at 400° for 10 minutes. Uncover and return pan to oven; bake an additional 18 minutes or until carrots are tender, turning once.
Why? Covering the pan creates a mini oven within the oven and speeds up roasting. It's essential to remove the foil early on to prevent buildup of steam from the vegetables' own juices.
Gotta agree with the other reviewers, two carrots is sort've a sad looking serving size. It's almost more like a garnish! So, I'd also add more carrots next time I cook this. Serving size aside, this is a tasty recipe. Mine weren't as brown as I would like, and were perhaps a tad mushier than I would have preferred, but I think that is something that simply varies with carrot size, and overall this was still a simple and tasty way to put together a cheap and easy side dish.