In a large skillet, heat oil and saute onions until they begin to brown. Add lamb and brown, about 10 minutes. Pour a small amount of water into skillet and cook meat for 45 minutes or until tender. Salt and pepper to taste. Add potatoes and continue cooking for 10 additional minutes.
Remove from heat and add peas and carrots. (Mixture can now be cooled in the refrigerator and saved for later, or used immediately.) When ready to assemble, preheat oven to 350 degrees and grease a large baking dish.
Cut sheets of phyllo in half. Brush 3 sheets generously with butter and stack them. Keep unused sheets covered with a damp cloth until ready to use. Place 1/2 to 3/4 cup of lamb mixture at bottom center of phyllo sheets. Sprinkle cheese and dill over lamb mixture. Fold sides in, overlapping, and brush butter at seam; then roll up, jelly-roll fashion. Place in prepared pan with seam down and brush butter on top of each roll.
Bake in preheated oven for 35 to 40 minutes or until golden brown. Makes 6 servings. Enjoy!