In a large, non-stick skillet, cook beef until browned. Transfer meat to a plate, discarding any fat remaining in the skillet. Heat the oil in the skillet over medium heat. Add onions and carrots, cover and cook until vegetables begin to soften (about 8 minutes). Increase heat to medium high. Add mushrooms and thyme and cook, uncovered, stirring occasionally, until mushrooms are soft. Return beef to the skillet. Stir in flour, then add the broth, 1/4 tsp salt and a pinch of pepper, and bring to a simmer. Stir in peas and corn. Pour mixture into a shallow 9" x 13" baking dish. Preheat oven to 350F. Peel potatoes and cut into 2" chunks. Place in a steamer basket and steam for 20-25 minutes, or until tender when pierced with a knife. Transfer potatoes to a bowl, then mash until smooth. Stir in milk, butter (or margarine), remaining 1/4 tsp salt and a pinch of pepper. Spread potato mixture on top of the meat. Sprinkle on a little paprika and parsley, if desired. Bake until heated through, about 25 minutes.