Pre cook sausage bits until browned. Remove from pan with slotted spoon.
Put chopped onion, bell pepper and thyme into pan. Sweat for 5 minutes
Add potato/sweet potato, season with S and P. reduce heat to low. cover and cook until potato is tender, stirring occasionally, about 10-20 mins
Increase heat to med high. stir sausage, beets, and half of parsley into potato. cook without stirring until hash begins to brown on bottom, about 5 mins. sprinkle cheese over. remove from heat. cover and let stand 5 mins
Fry up some eggs.
Divide up hash among 4 plates. put fried egg on top of each; sprinkle fresh parsley.