Combine the carrots and potatoes in a medium saucepan and cover with water. Season the water generously with salt and toss in the cinnamon stick and garlic. Bring the water to a boil and boil until the carrots and potatoes are fork tender. Remove from the water.
Place the butter in a small saute pan and cook until the butter is melted, browned and smells like hazelnuts. Remove from the heat and stir in the ground cumin, nutmeg and cayenne.
Pass the carrots and potatoes through a food mill. Stir in the spiced butter vigorously. Taste and make sure the carrot puree is delicious. Re-season if needed. Serve hot.