Ingredients:
1 1/2 cups(180 grams) bread flour, plus more as needed
1 teaspoon(5 grams) kosher salt, divided
1/3 cupwhole milk
1 large egg, lightly beaten
3 tablespoonsunsalted butter, softened, divided
1 tablespoonneutral oil, such as canola
2 medium yellow onions, peeled, halved crosswise, and thinly sliced into half-moons
1 large (10 ounces/(300 grams) Russet or Yukon Gold potato
2 tablespoonsmayonnaise, preferably Japanese-style like Kewpie
Freshly ground black pepper
1 cup(100 grams) low-moisture mozzarella cheese, shredded
Directions:
In a large bowl or the bowl of a stand mixer fitted with the dough hook, sift in the flour and 1/2 teaspoon salt. Make a well in the bowl, and add the milk and egg. Mix with a spatula or a bowl scraper until it forms a shaggy dough, then knead with your hands or the dough hook until the dough is smooth, 4 to 5 minutes. Add 2 tablespoons of the butter to the dough, and knead it for another 2 to 3 minutes to incorporate, until it forms a smooth, slightly tacky but not sticky dough. Form the dough into a ball and cover the bowl with a kitchen towel.
Heat the oil in a large skillet over medium-low heat. Add the onions to the pan with 1/4 teaspoon salt. Cook for 20 to 30 minutes, stirring occasionally and adding a splash of water if they start to stick to the pan or singe, until the onions have shrunk significantly and are deeply browned and caramelized. Remove from the heat and let cool slightly.
Fill a medium saucepan with water and bring to a boil over medium high heat. Peel the potato, quarter it, then boil for 15 minutes, or until knife-tender. Drain the potatoes and transfer to a medium bowl. Mash immediately with a potato masher or fork until very smooth. Mix in the mayonnaise, a few cranks of black pepper, and 1/4 teaspoon of salt.
Split the dough in half and reshape it into a ball. Place one piece of dough on a floured work surface and roll out into a circle about 10 inches in diameter. Repeat with the other piece of dough.
Sprinkle half of the mozzarella cheese over one dough, leaving a 1/2-inch border around the edge. Spread the mashed potatoes over the cheese in an even layer. Spoon the caramelized onions over the mashed potatoes in an even layer. Sprinkle the remaining cheese over the onions. Place the other dough circle on top, and pinch all around the edges of the dough to seal. To make it a bit neater, tuck the top edges just underneath the bottom. If the dough looks uneven, you can gently smooth it out with a rolling pin, shaping it into a neat, flat circle.
Melt 1/2 tablespoon of butter in a large skillet over medium-high heat. Using two wide spatulas, carefully slide the filled bread into the pan, cook for about 5-10 minutes, until the bottom is browned and crisp. Brush 1/2 tablespoon of butter onto the top of the bread, then carefully flip it over to cook for another 5-10 minutes, until browned and crisp.
Transfer the bread onto a cutting board or serving plate, slice it into wedges, and serve immediately.