For the pork: Preheat the oven to 400 degrees F. Drizzle the oil over the pork and sprinkle liberally with salt and pepper. Transfer the pork to a rack over a heavy-bottomed roasting pan. Roast the pork until a meat thermometer inserted into the thickest part of the loin reads 140 degrees F, about 1 hour.
Let the pork rest for 10 minutes. Set aside 1 1/4 pounds for the soup, cut into 1/2-inch chunks, and then reserve the rest for another recipe.
For the soup: Roast the poblano over a flame until charred all over. Place the poblano in a bowl and cover with plastic wrap until it softens. Once cool enough to handle, remove the charred skin from the poblano as well as the stem and seeds. Cut into a 1/4-inch dice.
Add the oil to a large Dutch oven or saucepot over medium heat. Add the onions and sweat until translucent and fragrant, about 8 minutes. Add the garlic and poblano and cook for 3 to 4 minutes. Add the coriander and cumin and cook until slightly darkened and fragrant, 2 to 3 minutes. Add the salsa verde and cook until it just comes to a boil, about 2 minutes. Add the stock and bring back to a boil.
Meanwhile prep all of your garnishes.
Once the soup comes to a boil, continue to cook for 5 minutes to allow the flavors to develop. Sprinkle with salt and black pepper.
When you are ready to serve, add the roasted pork just to heat through. Serve over rice and with any or all garnishes.