In Dutch oven, or deep, large pot, heat 2 tablespoons vegetable oil over medium heat. Add half of the meat, making sure not to crowd the pan. Cook meat, turning once, until nicely browned, about 5 minutes per side. Remove browned meat from pot and repeat with remaining meat.
When all the meat is browned, return all meat to pot, and add 1 cup of the sliced onions and 2 cloves of the minced garlic. Add 1 1/2 cups of water and 1 teaspoon salt. Stir well, bring to a boil, then reduce heat to medium low. Cover pot and cook for 30 minutes, undisturbed.
While you are simmering meat, bring 2 quarts water to a boil in medium saucepan. Plunge tomatoes in boiling water only for 2 minutes, to loosen skins. Remove them from the water and place them in a bowl and let cool. Once cool, peel and seed tomatoes, reserving the seeds, peels and any juices they may have released. Chop tomatoes and reserve.
In the same water where you blanched tomatoes, cook new potatoes, adding a bit of salt, and cook until potatoes are almost tender, about 15 minutes. Drain and reserve.
When meat has been simmering for 30 minutes, extract 3/4 cup of braising liquid with a small ladle. Place reserved tomato seeds, peels, and juices in blender container along with braising liquid, the chipotle chil, and Mexican oregano. Blend until very smooth and then pass through a strainer. Reserve this sauce.
In large frying pan, heat remaining vegetable oil and sauté remaining onions until softened, about 2 minutes. Add garlic and continue cooking until vegetables are totally limp but not browned, about 4 minutes. Add diced tomatillos and chopped tomatoes to the pan. Add 1/2 teaspoon salt and cook, until tomato mixture is soft, about 12 minutes.
Add cooked tomato mixture to meat mixture in Dutch oven, along with the reserved blended sauce. Mix well. Add cooked new potatoes and simmer for at least 10 minutes, to let flavors blend. Taste and adjust salt.
Serve hot in shallow bowls with a mound of white rice and corn tortillas.