In a heavy bottomed skillet, heat olive oil over medium high heat. Add onions and cook until they soften. Stir in garlic and pork. Cook until pork browns, stirring often, about 5 minutes. Stir in tomato paste and cook for 1 minute. Add chili powder, cumin, paprika, red pepper flakes, and salt. Stir to coat and let cook for 1-2 minutes more. Add in black beans and vegetable broth. Bring to a boil, reduce heat, and simmer for 5 minutes.
Add in corn and almost all the tomatoes, leaving a few for a garnish. Simmer for an additional 5-7 minutes, until tomatoes have softened but still keep their nice green color.
Serve chili with a dollop of sour cream, some cilantro, and a few fresh green tomatoes on top.