Combine salt, pepper, and mustard with the pork, beef, lamb, and chicken in separate bowls. Cover and refrigerate for at least 4 hours or overnight.
Boil the carrots, celery, and garlic in water until tender (about 20 minutes). Blend into a smooth puree and set aside.
Heat oil or lard in a large pot. Add onions and a pinch of baking soda. Cook over medium heat until golden and caramelized, about 10 minutes.
Sear the marinated beef first, followed by pork, lamb, and chicken, browning each for 5-7 minutes. Add water if needed to prevent sticking.
Add the bay leaves, blended vegetables, tomato paste, chili peppers, and the remaining mustard. Stir to combine. Pour in enough water to just cover the meat.
Cover and cook on low heat for 2 hours, stirring occasionally and adding water as needed to keep the meat submerged.
Stir in the red wine and let it simmer uncovered for 5 minutes to burn off the alcohol.
Mix in the sweet paprika, cover, and continue cooking for another 45 minutes.
Taste and adjust seasoning with salt, pepper, or additional chili. Ensure the meat is tender and falling apart.
Ladle into bowls and serve with fresh bread or polenta.