Heat large sauté pan with olive oil. When oil starts to smoke, put in all ingredients and cook until everything is translucent, stirring frequently. Set aside to cool. This may be made a day ahead.
Pre-cook the potatoes
Rub potatoes with oil and bake in 350°F oven until tender, about 40 to 45 minutes. Remove from oven and cool, and then large dice. This also may be made a day ahead of time or use leftover bakers.
To make Hash: In large skillet or rondo, heat butter over medium heat; add diced potatoes and sauté until they start to brown. Stir in braised pork and brown slightly. Next add sofrito, tomato, oregano and small amounts of the stock, letting it reduce down each time before adding more. When all ingredients are hot and mixed well. Stir in parsley and set aside but keep warm.
To Serve: For each serving, spoon 1 cup hash onto plate and top with the one poached egg and garnish with a sprig of oregano.