Preheat oven to 350 degrees. Cook carrots in chicken stock for ten minutes and then drain. In medium saucepan melt butter. Add onions and saute five minutes over medium heat. Sprinkle salt and pepper over the onions and then reduce heat. Add cheese, eggs and milk and cook until cheese melts. Fold in carrots and pour into a greased 1 1/2 quart casserole dish. Bake 45 min.