Toast bay leaves, cloves, fennel seeds, red pepper flakes, and whole peppercorns in a dry small skillet over medium heat, tossing often, until fragrant, about 2 minutes. Let cool; transfer to a spice mill (or mortar and pestle) and finely grind.
Preheat oven to 250°. Heat oil in a medium ovenproof pot over medium-high. Add livers and stir to coat; season with salt and pepper. Cook, stirring occasionally, until livers are deeply browned (they will look almost burned), 5–8 minutes.
Add onion, thyme, and Mama Lil's peppers; stir to coat. Taste and adjust seasoning with salt and pepper and cook, stirring as needed, until onion is golden brown and soft, 5–8 minutes. Add garlic (adding garlic after onion has been going for a while will keep it from burning) and stir to coat. Cook, stirring often, until garlic is soft, about 2 minutes. Stir in spice mixture and 1½ tsp. salt (this will toast the spices one more time, deepening their flavor).
Add tomatoes and wine, stirring and scraping up any browned bits. Mix in beef and pork (mixture will be fairly stiff, but will soften and loosen as it cooks). Add milk and mix well; everything should be evenly coated. Cover pot and braise in oven 6–8 hours. (Resist the urge to check on it. It's fine! We promise!)
Remove pan from oven. As the sauce cooks, it will firm up (looking somewhat like meatloaf); stir sauce to loosen. Pluck out thyme and, using an immersion blender, puree sauce until mostly smooth. Add vinegar; taste and season with more salt and pepper as needed.