HEAT fryer to 350° F. MIX together mashed potato, mushrooms, cheese, onions, salt and pepper until combined.
SCOOP potato mixture into the palm of your hand, cupping to create a bowl shape. PLACE a hard-boiled egg in the center and gently WRAP and seal tightly. Set aside to chill.
Put flour, whisked eggs and bread crumbs in three SEPARATE containers. TOSS each coated egg in flour, then egg wash, then bread crumbs.
FRY eggs, two at a time until golden, approximately 2 minutes each.
In a small bowl, WHISK together mustard, creme fraiche and vinegar and season with salt and pepper. DOLLOP onto a plate and place fried eggs on top.