In a 5- or 6-quart pot set over medium heat, heat olive oil until hot and rippling. Add the onion, bell pepper, celery and garlic, and cook for 3 to 4 minutes, until the onions start to soften.
Add the ground meat and cook, breaking the meat into small pieces, until no longer pink, 5 to 6 minutes. Drain excess grease.
Add beef broth or stock, bay leaves, dry mustard and cayenne pepper. Bring to a simmer and cook until the liquid is reduced by about half (give or take). If it doesn't noticeably reduce after about 25 minutes, proceed with the recipe.
Puree the stewed tomatoes in a food processor or blender. Add to the pot with the beans, sun-dried tomatoes, brown sugar, creole or cajun seasoning, and balsamic vinegar. Stir to combine.
Bring to a simmer and cook over medium-low for two hours, stirring occasionally and moderating heat as needed. Remove from heat. Taste and add salt, if needed (this is important!). This chili tastes even better a day or two after it is made. It can be reheated in a slow cooker or on the stovetop.
Notes
Sun-Dried Tomatoes: I use jarred sun-dried tomatoes in this recipe. Drain and lightly rinse the sun-dried tomatoes before chopping. The original recipe called for two cups chopped sun-dried tomatoes. Over the years, I've reduced that to one cup, based on personal preference, but you can add the full two cups, if you prefer. You can also use sun-dried tomatoes that need to be rehydrated. Simply rehydrate, chop, measure, and use in the recipe.