Choose a skillet or sauté pan in which you’ll be able to brown all the beef cubes without overlapping. If you have no pan quite that large, plan to do the meat in two stages. Put in the vegetable oil, turn on the heat to high, and when the oil is quite hot, slip in the meat. It should sizzle as it goes in if the oil is hot enough. Turn the meat over to brown it evenly on all sides, then use a slotted spoon or spatula to transfer it to a bowl.
Into the pan put the cut-up onion and some salt. Cook, always at high heat, for 2 or 3 minutes, stirring occasionally, until the onion becomes colored a tawny gold. When the onion is partly cooked—it must not become tender at this stage—transfer it with a slotted spoon or spatula to the bowl containing the browned meat cubes.
Choose a large lidded saucepan or casserole made of heavy ware, such as enameled cast iron. Put in the olive oil, the meat and onions, the bell peppers, salt, and liberal grindings of black pepper. Turn on the heat to low and cover the pot. Cook at a steady but very gentle simmer for 1 hour.
Add the milk and cut-up potatoes, cover, and cook at a slow simmer for another 30 minutes, turning the contents of the pot over from time to time. Reposition the lid, setting it slightly askew, and continue cooking at a steady simmer for an additional 30 minutes. When done, the meat should feel very tender when tested with a fork; and the peppers and onion and some of the potatoes will have dissolved into a dense, creamy mixture.