In a large pot, add pork shoulder and cover with water. Sprinkle water with salt and simmer over medium heat for 20 minutes.
In a blender, add poblano peppers, onion, garlic, cilantro, and 1 cup of cooking water from pork. Blend until smooth. Drain any remaining water from pot and add sauce to pork. Simmer until pork is cooked through, 10-15 minutes. Remove pork.
Stir cream into sauce, add salt and pepper, reduce heat to low, and simmer for 25 minutes, stirring frequently.
Cut the pork into small chunks.
In a large frying pan, heat oil over medium heat. Fry each corn tortilla briefly on each side, 5-10 seconds. They should still be bendable.
Place a line of pork pieces near the edge of a corn tortilla. Roll the tortilla and place on serving plate. Repeat with remaining tortillas. Top with poblano sauce, sour cream, tomatoes, and green onions. Serve immediately.