In a large Dutch oven or stockpot over medium-low heat, add olive oil, onion and poblano. Sauté 4 to 5 minutes, stirring occasionally, until veggies are softened. Add chorizo, breaking up the meat with a spoon until crumbly. Cook about 8 to 10 minutes or until meat is browned. Add garlic, and cook an additional 1 to 2 minutes until fragrant.
Add diced tomatoes, tomato sauce, tomato paste, beans and water. Stir until combined, and let chili come to a low boil. Reduce heat to low. Add seasonings, adjusting to taste, and let simmer for at least 20 minutes. The longer it simmers, the more the flavors will develop. Fold in 1 cup shredded cheese and stir until cheese melts into the chili.
To serve, ladle into bowls and garnish with toppings of choice. Garnish with remaining cheese if desired.