In a blender or food processor, pulse the cooked beet, flour, milk, egg, vegetable oil, and vinegar until smooth. Pour the batter into a bowl and set aside for 30 minutes.
Combine the cinnamon with the sugar and mix well.
Heat an oiled non-stick skillet over medium heat. Pour in enough batter to cover half of the skillet. Tip and rotate the skillet until the batter covers the entire area.
Cook until the batter turns from wet to moist, and the edges begin to curl away from the sides of the skillet.
Turn the pancake over, and continue cooking until lightly golden on the other side. Place the pancake onto a plate, and cover with a kitchen towel to keep moist.
Repeat with the remaining batter, lightly oiling the skillet as needed to keep the pancakes from sticking.
Sprinkle the cinnamon sugar over the pancakes.
Roll up the pancakes and serve with the orange quarters.