In a large Dutch oven over medium heat, add the oil and coat the bottom of the pan.
Add the onion, and sautee until soft, about 4 minutes.
Add the garlic and cook 30 seconds longer.
Stir in the tomato paste to coat the veggies.
Add the Cumin, Espresso chili powder, Dark Chili powder or Ancho powder, salt, pepper, garlic powder, and brown sugar.
Whisk in the beer slowly, scraping up any browned bits as needed on the bottom.
Add the crushed tomatoes, leftover pulled pork, and black beans.
Bring to a simmer and let the flavors mingle for about 45 minutes to 1 hour.
Remove from heat and add the juice from the lime.
Cover the Dutch oven to keep the chili warm.