Preheat oven to 400 degrees. Line a rimmed baking sheet with foil or parchment paper. Cut carrots if using large carrots into 3" pieces (halved or quartered lengthwise if large).
Spread out carrots on the foil. Evenly top with butter, brown sugar, syrup, and red pepper flakes. Toss to combine.
Bake carrots, tossing every 20 minutes, until tender and browned around the edges, 50-60 minutes. Transfer to a platter. Sprinkle with sea salt (if using).