Heat olive oil and butter in a large heavy skillet over medium heat; crowd in the cubed corned beef and potatoes. Spread evenly in the pan and increase heat to high or medium high. Cook for 3 or 4 minutes and add in peppers and onions. Do not stir the potatoes and corned beef; let them brown until sizzling. Use a spatula to peek underneath to check browning. If there is too much sticking, add a little more oil to the pan. Continue to cook in this manner until the potatoes and the corned beef are browned and crispy on the bottom. Once browned, add water, then cover with a lid and steam until water evaporates (about 2 to 3 minutes). Remove from heat and serve topped with fried or poached eggs.