Heat oil in a skillet; add sliced beets and salt, and sauté briefly. Add water to cover bottom of skillet, lower heat, cover, and cook for 20-30 minutes or until beets are nearly tender. Add more water if needed to prevent scorching.
Add mirin, cooking for 5 more minutes, then add soy sauce and cook for another minute.
Dissolve kuzu in 1 Tbsp water and add to beets while stirring constantly until liquid returns to a simmer. Cook 1-2 more minutes, adding a little more water if too thick. Serve hot.