Preheat oven to 450°F. Prick potatoes several times along top with tines of a fork then roast 1 hour or so, until very tender.
When potatoes are just cool enough to handle, split them lengthwise and scoop out the flesh into a ricer or food mill, or push it through a fine strainer into a bowl (you will need to do this in batches). Warm EVOO in a small skillet or pot then melt butter into oil; add to potatoes. Season with salt, pepper and nutmeg then add cheese and 1 cup flour. Mix to combine. Using your hands, work in the egg yolks so they are evenly distributed throughout.