Add the bacon to a large Dutch oven set over medium high heat, and cook stirring often until the fat's rendered and the bacon's cooked. Using a slotted spoon transfer the bacon to a paper towel lined plate, and set aside.
Add the onions to the pot, and (stirring often) let them cook for 8-10 minutes until they've softened and begun to turn translucent.
Add the garlic to the pot, stir, and let it cook for 60 seconds- just until fragrant.
Add all of the spices/seasonings EXCEPT the rub to the pot, stirring to evenly mix them with the onions and then stir in all three cans of tomatoes & the beef broth until evenly incorporated.
Add the peppers & beans to the pot, stirring until incorporated.
Bring the mixture to a boil, and then immediately reduce the heat to a low simmer. Add the lid to the pot, but so that it's cracked to allow steam to escape.
Check that the mixture's at a nice simmer, and then let it cook for 2 1/2 - 3 hours- stirring every 30 minutes or so and recovering when done.
Once the beans are tender, reduce the heat even further until the chili's at the lowest simmer possible- then add the dry rub, brisket, and bacon stirring until evenly incorporated.
Let the chili simmer for 30 more minutes, uncovered, before serving.