Preheat an oven to 500 degrees F (260 degrees C). Line a baking sheet with aluminum foil.
Roast tomatoes in preheated oven on the prepared baking sheet until completely softened, about 25 minutes. Transfer tomatoes to a cutting board to cool.
Spread chopped carrot onto the prepared baking sheet; season with a pinch of cinnamon and salt.
Roast carrots in preheated oven until tender, about 25 minutes.
Heat a large skillet over medium-high heat. Toast onion slices, garlic cloves, and jalapeno pepper in the skillet until beginning to char, 5 to 7 minutes.
Peel cooled tomatoes and put in a blender bowl; add onion, garlic, jalapeno pepper, Sriracha chile sauce, and 1 1/2 teaspoons cinnamon and puree until smooth.
Heat vegetable oil in a large stockpot or Dutch oven over medium-high heat. Stir pureed tomato mixture into the oil; cook and stir until the mixture thickens, about 5 minutes.
Pour water into the pot; add chicken bouillon and stir. Bring liquid to a simmer, reduce heat to medium-low, and cook mixture, stirring occasionally, until the liquid reduces slightly, about 15 minutes.
Stir chicken and black beans into the soup; bring again to a simmer and cook until beans are softened, about 15 minutes. Add carrots and cook to reheat the carrots, 2 to 3 minutes. Season soup with salt and pepper.