1. Soak chile negro in at least 1 cup of hot water 20 minutes, up to an hour. Remove chile from water, reserving liquid. Remove seeds and stem from chiles. Puree cleaned chiles in a small food processor along with 1/2 cup of roughly chopped cilantro stems, garlic, and 1/2 cup of soaking liquid. Puree to fine paste, adding more liquid as necessary.
2. Meanwhile, heat 2 Tbsp of olive oil in a large lidded Dutch oven over a medium-high flame. Saute onion and carrots until soft, about 5 minutes. Add chili powder, cumin, oregano, and 1 tsp of salt. Cook until fragrant, about 2 minutes, contents should be nice and toasted. Carefully pour in tomatoes and bring to simmer.
3. Add sweet potatoes, parsnips, black beans, black chile paste, and remaining soaking liquid. Stir to combine and bring to a simmer, adding one or two cups of water if necessary to make soupy. The chili will thicken as it simmers.
4. Simmer, partly covered for 20 minutes, until potatoes and parsnips are tender. Season with salt and cayenne pepper to taste. Simmer 5 minutes more.
5. To serve, ladle the chili into bowls and garnish with cilantro leaves, sour cream, and jack cheese.