Place a large Dutch oven or heavy-bottomed pot over medium heat. Add the sliced andouille and cook for 4 to 5 minutes, stirring occasionally, until browned around the edges. Transfer the sausage to a plate, leaving about 1 tablespoon of rendered fat in the pot. Add the cooking oil only if the pot is dry.
Add the onion, bell pepper, and celery. Cook for 5 to 6 minutes, stirring occasionally, until they begin to soften. Add the optional jalapeño and cook for 1 minute. Stir in the garlic and cook for 30 seconds.
Add the tomato paste and cook for 1 to 2 minutes, stirring constantly, until it darkens slightly. Stir in the smoked paprika, Creole seasoning, thyme, cumin, black pepper, and optional cayenne. Cook for about 30 seconds, just until fragrant.
Reduce the heat to medium-low. Add the 2½ pounds of Dolores Chili Brick and break it into smaller pieces with a sturdy wooden spoon. Pour in 1 cup of beef broth and stir frequently until the brick has melted into a smooth, thick base.
Return the browned andouille to the pot. Stir in the pinto beans, kidney beans, diced tomatoes with green chiles, Worcestershire sauce, and bay leaf. Add up to ½ cup more broth as needed to reach the desired consistency.
Bring the chili to a gentle simmer. Reduce the heat to low, partially cover the pot, and cook for 25 to 30 minutes, stirring occasionally so the bottom does not stick. For thicker chili, uncover the pot during the final 10 minutes.
Remove and discard the bay leaf. Taste before adding salt, then adjust with additional Creole seasoning, black pepper, or cayenne if desired. Ladle into bowls and serve with cheddar, green onions, sour cream, jalapeños, cornbread, or crackers.