Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Slice the bell peppers into wide, triangular pieces to serve as the 'chips' for the nachos.
In a small bowl, toss the shredded cooked pork shoulder with olive oil, smoked paprika, garlic powder, sea salt, and black pepper until well coated.
Arrange the bell pepper chips in a single layer on the prepared baking sheet.
Distribute the seasoned pork and the rinsed black beans evenly over the pepper chips.
Sprinkle the shredded sharp cheddar cheese over the top of the pork and beans.
Bake for 8 to 10 minutes, or until the peppers are just tender and the cheese has completely melted.
Remove from the oven and drizzle the salsa verde over the nachos.
Garnish with freshly chopped cilantro and a squeeze of lime juice before serving warm.