Heat 1 1/2 teaspoons oil in a Dutch oven over high heat. Season pork with salt and pepper and add half of it to the pot. Cook, stirring occasionally, until browned on all sides, 4 to 6 minutes. Transfer the meat to a plate lined with paper towels; repeat with another 1 1/2 teaspoons of the oil and the remaining meat.
Reduce the heat to medium and add the remaining 1 1/2 teaspoons oil; heat until hot. Add onion and bell peppers; cook, stirring, until the vegetables begin to soften, about 5 minutes. Add tomato paste, garlic, cumin, chipotle (or jalapeños), and oregano. Cook the mixture, stirring, until fragrant, about 2 minutes. Slowly stir in beer, scraping up any bits from the bottom of the pan. Simmer for 2 minutes.
Stir in beans, tomatoes and their liquid, and the reserved pork; bring to a simmer. Reduce the heat to low, cover and simmer, stirring occasionally, until the pork is tender and the sauce has thickened slightly, about 30 minutes. Add lime juice and season with salt and pepper. Garnish with scallion greens or cilantro and serve.