Strain the cabbage, reserving the liquid. Heat the foie gras fat in a large heavy-bottomed saucepan or Dutch oven over medium-low heat and add the onion, chili flakes, and cinnamon stick. Cook, stirring, without coloring, for 10 minutes. Add the cabbage and cook, stirring occasionally, for another 10 minutes. Add the marinating liquid, bring to a boil, and cook at a light simmer, stirring occasionally, until the cabbage is tender and the liquid is reduced to a syrupy consistency, about 45 minutes. If needed, add spoonfuls of water if the liquid glazes before the cabbage is tender. Stir in the butter and adjust the seasoning with salt and pepper; reserve, warm.