Chop up the poblano, hot pepper, and onion. Press the garlic. If you don't have a garlic press, then chop it into small pieces.
To a large stock pot, add 1 tablespoon of vegetable or olive oil. Add the poblano pepper to the pot first. It takes longer for them to soften up than the onion. Saute for a few minutes, then add the onions. Add the ground beef after about a minute.
Cook the ground beef through, breaking it up into pieces as it cooks. I like to use the higher-fat ground beef, which means I also have to remove some of the fat from the pan. I just tilt the pan a bit and spoon out some of the grease with a large serving spoon.
Before adding the beans to the chili, rinse them in a strainer to remove some salt. I buy low-sodium beans, but I still like to rinse the beans off to remove as much excess salt as possible. You don't have to do this, it is just something I like to do. Reserve about two tablespoons of the bean juice to add to the chili to help thicken it.
Once the ground beef has cooked through, add the 2 cups of broth, black and kidney beans, tomato sauce, hot pepper, garlic, and spices. Mix to incorporate.
Let the chili simmer on medium heat for 20 minutes. Smash a few of the beans on the side of the pot and stir back into the chili. This helps to thicken the chili.
Serve hot and enjoy! Add shredded cheese, sour cream, diced onions, or crushed corn chips if desired.