Preheat oven to 400F.
Start the mashed potatoes: Peel and cut potatoes (1/2 inch or quartered). Place in pan and cover with cold water (1/2 in over potatoes). Set over high heat, cover and bring to a boil. [start step 3 then return to potatoes] ((Once boiling, uncover, decrease the heat to maintain a simmer and cook until tender and easily crushed with tongs, approximately 15-20 mins.))
In a large saut pan with oil, saut onions and carrots, then garlic. Add ground beef and cook through until brown.
Continue filling: Sprinkle meat with flour and toss to coat. Add salt/pepper and cumin (optional), add Worcestershire Sauce, Beef Broth, and Rosemary/ Thyme (optional). Brind to boil, cover and simmer low and covered until sauce is thick (10-15 mins).
Mash Potatoes: Add half-and-half or milk, butter, and salt/pepper to drained potatoes. Mash until smooth.
Continue filling: Add corn and green beans (peas optional) for just a few mins to heat.
Combine in lightly greased 3 qt casserole dish: Beef filling on bottom. Sprinkle layer of cheese on top. Top with mashed potatoes. (Make sure the potatoes seal the beef filling in so it doesn't boil and create a mess.) Use a fork to make rivets on the top of the mashed potatoes. Add small amount of paprika on top.
Bake dish for 25-30 minutes in oven at 400F. Let cool (about 15 mins).