In a large pot or dutch oven, heat oil over medium-high heat. Add the diced onions, bell peppers, poblano pepper, zucchini, and garlic. Saute, stirring occasionally, until vegetables begin to soften, about 4 minutes.
Add the meat and cook, breaking up the meat with the back of a spoon, until it is no longer pink. Drain off excess fat and return to the pot over medium heat.
Add the salt, pepper and tomato paste and stir until well combined. Then add the tomato sauce, diced tomatoes, beef broth, chili powder, paprika, and cumin to the pot. Bring to a rapid simmer, then reduce heat so that the chili it is gently simmering on low to medium-low heat.
Simmer, uncovered and stirring occasionally, for at least 1 hour (I sometimes cook it for up to 4 hours, the longer the better!). The chili should reduce a bit and thicken (if you like yours more soupy, simmer it covered).