In a large Dutch oven or heavy stock pot, heat the oil over medium-high temperature. When the top of the oil is shimmering, add half of the pork.
Allow it to sit in the hot pan to develop a sear before stirring; allow to brown. Remove from pan to a plate. Repeat for the second half of the pork.
Add the onions to the pan and sauté until softened (2-3 minutes). Add the garlic and stir together.
Return the meat (and any accumulated juices on the plate) to the pan along with the chicken stock, potatoes, salt and green chilies.
Bring to a boil, reduce temperature to allow stew to simmer. Simmer for 1 hour. Serve garnished with torn cilantro leaves, diced red pepper and a bit of grated cheese if desired.