Combine the water, unsalted butter, and a pinch of kosher salt in a saucepan over medium heat. Bring to a boil.
Add the all-purpose flour all at once and stir continuously until a smooth dough forms. Continue cooking for 1 to 2 minutes to remove the raw flour flavor.
Transfer the dough to the bowl of a stand mixer fitted with a paddle attachment. Mix on medium-high speed to release some of the steam.
Add the eggs one at a time, allowing each egg to fully incorporate before adding the next. Continue mixing until the Parisian gnocchi dough is smooth, glossy, and thick. You should have approximately 500 g of dough.
Steam the Yukon Gold potatoes until fork tender. While still warm, pass them through a potato ricer and measure out 500 g of riced potatoes.
In a large bowl, combine the riced potatoes, prepared Parisian gnocchi dough, shredded aged white cheddar, dried scallions, freshly cracked black pepper, and kosher salt. Mix until fully incorporated. The potato puff mixture should be thick, smooth, and scoopable.
Heat rice bran oil or another neutral frying oil to 350°F.
Using a small portion scoop or melon baller, dip the scoop into the hot oil between portions to help release the dough. Carefully scoop portions of the mixture into the hot oil.
Fry the potato puffs until deeply golden brown and crisp on all sides. Transfer to a wire rack or paper towel-lined tray and season lightly with kosher salt while still hot.
Place the hot potato puffs into a serving bowl and add plenty of cheese curds. Transfer to a serving platter and finish with chopped chives or scallions, fresh cracked black pepper, and warm au jus.
Serve immediately while the potato puffs are hot and crisp and the cheese curds begin to soften.