In a large dutch oven over medium heat, heat 2 tbsp. Olive oil. Season ribs with 1 tsp. Salt. sear ribs on each side, including their thin, bone in side, 3 to 5 minutes each. Remove from pan and set aside.
Add onion, garlic, and basil into pan. Cook until onion and garlic are softened and slightly golden around the surface, 7 minutes. Season with ½ tsp. Salt. Adjust heat as needed.
Add white wine and bring up to a simmer. Cook until the wine is nearly reduced. There should be a small amount of liquid in the bottom of the pan. It will look like the onions are soggy at this point-- that’s good! About 3 minutes.
Add the sauce and give the mixture a stir. The sauce will start to bubble quickly. Add the pork back in and submerge in the sauce. Turn heat to medium low, cover and cook until tender and falling off the bone, 35 to 45 minutes.