When vegetables are prepared this way, their surfaces remain firm to the touch and may appear undercooked -- but never fear, they'll be tender inside. If you let them cook until they're soft to the touch, they'll be mushy within.
Preheat grill for direct-heat cooking, or build a fire and burn down wood until only red coals and gray ash remain.
Place vegetables directly on coals and cook, turning occasionally, until blackened all over and tender enough to be pierced with the tip of a knife with some resistance, about 15 minutes for carrots and peppers, 25 minutes for beets and onions. Place peppers in a bowl, cover, and let stand 10 minutes. Let other vegetables cool slightly while peppers steam.
Rub peppers and other vegetables with your hands or paper towels to remove as much of charred exteriors as possible. Halve carrots lengthwise, and slice peppers into strips, discarding stems and seeds; slice beets and onions into wedges. Drizzle with oil, season with flaky salt, and serve with dressing.