Peel and slice potatoes into 1/4-inch thick slices.

Heat broiler to high.

In a large cast iron or non-stick, oven-safe frying pan, heat oil over medium heat, until shimmering, about 3-4 minutes.

Add potatoes, cauliflower mixture, and 1 teaspoon salt to hot oil and gently move vegetables around in the oil to coat, then spread into an even layer. Oil should gently bubble up over vegetables, if it is bubbling too rapidly, turn heat to medium-low or low.

Gently stir vegetables occasionally and cook until potatoes are fork tender, about 15 minutes.

Set a strainer over a large, heat-safe bowl and pour potato mixture through the strainer, capturing excess oil in the bowl. Toss potatoes with beaten egg and remaining teaspoon of salt.

Wipe pan clean and return to stove over medium heat. Add 2 tablespoons oil back to pan and potato mixture.

Stir the first minute or so, scraping from the bottom of the pan to let egg cook. Then press down into a single layer. Let cook, undisturbed for about 4-5 minutes or until almost cooked all the way through but still a little runny in the middle.

Transfer to the broiler and cook until lightly browned and no longer runny in the middle, about 1-2 more minutes. Remove and let sit 10 minutes before removing from pan. Keep broiler on.

Run a spatula around the edges and bottom to loosen then flip onto a large plate. Serve in slices, warm or room temperature with romesco sauce.

Lay peppers in a single layer on a baking sheet. Char under a broiler until toasted and browned, flipping halfway through. This took 12 minutes under my broiler, but this will depend on the heat of your broiler. Let cool slightly.

Remove stem and seeds from peppers and place in a food processor with remaining romesco ingredients, except the olive oil.

With the food processor running, blend, and slowly add oil at the same time. Once blended and smooth, taste and add more salt or vinegar if needed.