No corned beef in this hash, only carrots, asparagus, peppers and onions with the potatoes.
Fill a medium saucepan with cold water, and add potatoes. Bring to a boil, reduce heat, and simmer for 5 minutes. Add carrots, and continue cooking until vegetables are just tender, 10 minutes more. Remove from heat, drain vegetables, and set them aside until cool enough to handle. Cut potatoes and carrots into 1/2-inch cubes.
In a large nonstick skillet, heat 1 tablespoon butter and oil over medium heat. Add onion, and cook until transparent and golden at edges, about 10 minutes. Add red peppers, and cook, stirring another 10 minutes, or until soft. Add half the thyme and rosemary. Add potatoes and carrots, and mix well. Cook over medium heat, stirring only occasionally, until a golden crust forms on potatoes, about 15 minutes.
Cut off asparagus tips, and cut remaining tender parts into 1/2-inch lengths. Discard woody ends. Add tips and pieces, remaining thyme and rosemary, and stock to skillet, and cook a few more minutes, until stock reduces and thickens slightly and asparagus is tender. Season to taste with salt and plenty of pepper. Transfer to a serving platter; keep warm.
Meanwhile, heat butter to taste in a clean skillet, and fry eggs. Serve eggs on a bed of hash, and sprinkle with scallions.
The vegetables can be prepared the day before and refrigerated in separate plastic bags.