Set a rimmed baking sheet on the center rack and heat the oven to 425°F so the pan gets hot.
Prep the vegetables: halve the brussels sprouts (quarter any very large ones) and cut the squash into 3/4-inch cubes for even roasting.
In a large bowl, toss sprouts and squash with olive oil, cinnamon, salt, and pepper until well coated.
Carefully pour the vegetables onto the preheated baking sheet, arranging sprouts cut-side down. Roast for 12 minutes.
Pull the pan, toss everything, and drizzle 2 tablespoons of the honey over the vegetables. Return to the oven and roast until deeply caramelized and tender, 10 to 12 minutes more.
While the vegetables finish, stir the remaining 1 tablespoon honey with the apple cider vinegar in a large bowl. Add the dried cherries and let them sit to lightly plump, 3 to 5 minutes.
Transfer the hot vegetables to the bowl with the honey-vinegar and cherries. Toss gently to gloss and season; adjust salt or pepper to taste and serve right away.