Mix grated potato, flour, baking soda, and salt into 1 cup mashed potatoes.
Gradually mix in enough buttermilk to form texture of firm mashed potatoes.
Heat heavy large skillet over medium-high heat until hot. Brush with oil.
Drop 1 heaping tablespoonful potato mixture into skillet. Using back of spoon, flatten mixture into 2-inch round. Repeat, forming 4 more rounds. Cook over medium-low heat until boxty is golden brown on bottom and slightly puffed, about 3 minutes. Turn and cook until second side is brown, about 3 minutes.
Transfer to baking sheet; keep warm in oven. Repeat with remaining potato mixture in batches, brushing skillet with more oil as necessary.