Wash salad greens, tear and place on paper towels to dry. In a small bowl, whisk together vinegar, mustard, salt and pepper. Slowly whisk in olive oil until completely combined. Set aside.
Grate peeled potatoes (onto a cutting board) using largest hole of grater. Heat (over medium high) enough peanut oil to coat the bottom of a medium skillet. Squeeze the liquid out of the grated potatoes and place into skillet. Season with salt and pepper. Watching carefully (the bottom will burn quickly) and shaking frequently, cook the "pancake" until the bottom is golden brown and the top begins to soften. Slide the pancake onto a cutting board and, if necessary, add additional peanut oil to the pan. Turn pancake back into pan and cook the reverse side until golden. Drain on paper towels and cut into wedges.
To assemble, toss greens with dressing to coat and divide evenly among four salad plates. Top with wedges of potato pancake (and drizzle with a small amount of dressing). Garnish with feta cheese and serve while potatoes are still warm. 4 servings.