Heat 2 Tbsp. lamb fat in same pot over medium-high (reserve remaining 1 Tbsp. lamb fat for assembling the moussaka). Add onion, cinnamon, 2½ tsp. salt, and ½ tsp. pepper and cook, stirring occasionally, until onion is tender and translucent, 8–10 minutes. Add chiles and remaining garlic and cook, scraping up any browned bits from the bottom of the pot, until onion is golden brown, about 5 minutes. Add paprika and tomato paste and cook until brick red in color, about 1 minute. Add wine and cook, stirring occasionally, until slightly reduced and no longer smells of alcohol, about 3 minutes. Add tomatoes and break up with a wooden spoon into small pieces (the seeds will shoot out at you if you’re too aggressive, so start slowly—puncture the tomato, then get your smash and break on!). Add lamb and remaining 1 Tbsp. mint and 1 Tbsp. oregano and cook, stirring occasionally, until most of the liquid is evaporated and mixture looks like a thick meat sauce, 5–7 minutes. Pluck out and discard cinnamon stick.