Scrambled Eggs with Prosciutto and Focaccia

1. In a small sauté pan, heat 1/4 inch of neutral oil just below medium-high heat until it begins to shimmer. Line a plate with paper towels. Lay 1 slice of prosciutto into the hot oil (be careful of the oil sputtering once the prosciutto is added) and fry until the prosciutto shrinks and becomes almost translucent, 30 seconds to 1 minute per side. Remove the prosciutto to the paper towels and season with pepper. Continue to fry all the slices, replenishing and reheating the oil as needed. The prosciutto will crisp up as it cools. Set aside while you prepare the eggs.
2. Crack the eggs into a large bowl and whisk until light, frothy, and uniform in color. Strain the eggs through a fine-mesh sieve into a separate bowl.
3. In a large nonstick sauté pan, combine the butter and crème fraîche. Pour the eggs into the pan and add the pepper flakes. Turn the heat to low and cook slowly, mixing frequently and gently using a silicone spatula or a wooden spoon until soft curds form. Depending on the strength of your burner, this can take anywhere from 15 to 35 minutes (sometimes even longer). Remove from the heat (the eggs will still be somewhat wet and have a custard-like consistency). Season with salt and pepper and gently fold in the Parmigiano.
4. Working quickly so that the eggs do not continue cooking in the hot pan, mound the eggs on top of the warm Focaccia and sprinkle with additional Parmigiano-Reggiano and pepper. Top with the crispy prosciutto and serve as open-faced sandwiches.

Focaccia:

1. Make the dough: In a medium bowl, stir together the water, yeast, and honey until dissolved. In a very large bowl, whisk together the flour and kosher salt, then add the yeast mixture and olive oil. Stir with a rubber spatula until just incorporated, then scrape the sides of the bowl clean and cover with plastic wrap. Leave out at room temperature until at least doubled in volume, 12 to 14 hours.
2. Spread 2 to 3 tablespoons of olive oil evenly onto an 18 × 13-inch sheet pan. When the dough is ready, use a spatula or your hand to release it from the sides of the bowl and fold it onto itself gently. Pour the dough out onto the pan, then pour an additional 2 tablespoons of olive oil over the dough. Using your hands, gently stretch the dough to the edges of the pan. (The best way to do this is to place your hands underneath the dough mass and pull outward.) The dough will shrink a bit, so repeat stretching once or twice over the course of 30 minutes to ensure that the dough remains spread out over the whole pan.
3. After the dough is stretched, using your fingertips, dimple the dough all over its surface.
4. Make the brine: Stir together the kosher salt and water until the salt is dissolved. Pour the brine over the dough to fill the dimples. Proof the focaccia, uncovered and at room temperature, for 45 minutes until the dough is light and bubbly.
5. Thirty minutes into this final proof, set one oven rack in the middle position and a second in the top position and preheat the oven to 450 degrees F. If you have a baking stone, place it on the middle rack. Otherwise, invert another sturdy baking sheet and place it on the middle rack. Allow the baking stone or baking sheet to preheat before proceeding with baking.
6. Sprinkle the focaccia with flaky salt. Bake directly on top of the stone or inverted pan until the bottom crust is crisp and golden brown, 25 to 30 minutes. To finish browning the top crust, transfer the focaccia to the upper rack and bake for 5 to 7 minutes longer.
7. Remove the focaccia from the oven and brush the olive oil over the whole surface. Let cool for 5 minutes, then release the focaccia from the pan with a metal spatula and transfer to a wire rack to cool completely.
8. Serve warm or at room temperature. For longer storage, wrap in parchment and keep in an airtight bag or container at room temperature for up to 3 days.