Preheat the oven to 450°F.
Bake the whole potatoes for 1 hour until completely tender.
Allow to cool just long enough to handle.
Scoop the flesh from the potatoes and pass through a ricer or mash until smooth.
In a bowl, combine the potato, egg, flour, baking powder, salt, white pepper, and chives.
Mix gently – just enough to bind without activating too much starch.
Heat a nonstick or cast-iron pan over medium heat with oil and butter.
Place a 2-inch ring mold in the pan.
Add a thin layer of potato mixture (about 1 tbsp), creating a base.
Place one yolk in the center.
Cover with more potato mixture, sealing the yolk completely.
Cook 3–4 minutes per side until deeply golden and crisp.
Carefully remove the ring mold after the first side sets.
Flip gently and cook the second side.
Finish with a knob of butter and baste lightly.
Transfer the pancake to a plate.
Spoon a small quenelle of crème fraîche on top.
Add a generous dollop of caviar.
Finish with chives and flaky salt if needed.