Heat Dutch oven or large pot over medium-high heat. Once hot, add onion and ground beef, breaking beef apart and mixing until no longer pink, about 7-8 minutes. Drain excess grease.
Add garlic and poblano pepper, cooking for about 2 minutes.
Stir in the tomato paste, chili powder, cumin, cayenne pepper, and salt. Cook for one more minute until all ingredients are coated in the tomato paste and spices.
Add diced tomatoes, tomato sauce, green chilies, and beans.
Bring to a simmer. Cover and turn to low heat. Check to be sure it's still simmering. Cook for 30 minutes, stirring occasionally.
If you want a thicker chili, take the top off and simmer for the last 5-10 minutes.
Serve with sour cream and shredded cheddar cheese!