Preheat oven to 375°. Trim carrot greens to about 2 inches, then scrub or peel carrots and heap in 2 rimmed baking sheets. Mix rum, maple syrup, and oil and pour over carrots. Mix cayenne, cumin, and 1 tbsp. salt, sprinkle over carrots, and turn them with your hands so everything gets distributed. Divide among 4 rimmed baking pans in a single layer.
Roast carrots (in two batches if you have one oven) until thoroughly tender and browned, 45 to 50 minutes depending on how big they are. Roll them over halfway through to brown evenly. If the pan starts getting dry, splash in 1/4 to 1/2 cup water.
Heap a layer of carrots on a rimmed serving platter. Scatter half of feta over them, then half of cilantro. Add the remaining carrots, then drizzle with juices from pan. Mix lemon, honey, and salt to taste and drizzle that on too. Sprinkle with the rest of the feta and cilantro.