Stir black beans, 1 cup chicken broth, tomato paste, and cumin together in a heavy pot over low heat; cook at a simmer until hot, 5 to 10 minutes.
Heat olive oil in a skillet over medium-high heat. Saute onion, green bell pepper, and jalapeno pepper in hot oil until the vegetables are softened, 5 to 7 minutes; add garlic and continue cooking just until fragrant, 1 to 2 minutes. Transfer to the pot with the beans and stir.
Stir sugar into the bean mixture, adding more chicken broth if you want more liquid in the final product; season with hot sauce and continue cooking at a simmer until the vegetables impart a savory flavor to the broth, 10 to 15 minutes.