Place sweet potatoes in a large pot of salted water, and boil until completely tender.
While the potatoes are cooking, place a large skillet or pot over medium-high heat. Add the oil and the onion, and cook for 3-5 minutes until the onion is translucent and browning at edges.
Add the beef to the onion, then sprinkle on 2 tsp. of salt, onion powder, and garlic powder. Mix the spices into the meat, breaking it up with a spoon, and allow to cook for an additional 5 minutes.
Add Worcestershire sauce, tomato sauce, and mixed vegetables, reduce heat and simmer for 15 minutes.
Once the sweet potatoes are cooked, drain and then return them to the boiling pot. Add butter, milk and remaining salt, and blend with an immersion blender until smooth. If you prefer lumpier potatoes, mash by hand using a masher.
Layer the meat mixture into a 9×13 casserole dish, then spoon the potatoes over the top, spreading to cover the meat completely.
Spread shredded cheese on top of the potatoes, and place under a broiler to melt until golden brown, 2-4 minutes.