Make the Mayonnaise: Anchor a bowl using a damp cloth underneath. Add the egg yolks, mustard, salt, and white wine vinegar to the bowl. Whisk until combined. Slowly trickle in the neutral oil in a steady stream while whisking continuously until thick and emulsified. Finish by whisking in the lemon juice. Set aside.
Marinate the Tomatoes: Slice the beefsteak tomato into medium-thick slices. Place in a shallow dish with the finely diced shallots. Season with flaky sea salt, black pepper, sherry vinegar, and rapeseed oil. Let it marinate for about 5 minutes to soften the shallots and draw out the tomato juices for a natural dressing.
Cook the Bacon: Place a skillet over medium heat. Add the streaky bacon and a splash of neutral oil. Render the fat slowly over medium-low heat for about 8 minutes until the bacon becomes crisp and golden. Transfer the cooked bacon to a plate, leaving all rendered bacon fat in the pan.
Fry the Center Toast: Place the thin middle slice of potato bread directly into the hot bacon fat in the skillet. Fry over low heat for about 2 minutes on each side until golden and crunchy, scraping up all caramelized bacon bits from the bottom of the pan.
Warm the Outer Bread: Optionally warm the 2 thick outer slices of potato bread in a dry pan for about 1 minute until soft and warm, but not fully toasted or dry.
Assemble the Sandwich: Spread a generous layer of homemade mayonnaise onto the bottom thick slice of bread. Layer on the marinated tomato slices, top with the softened marinated shallots, and add a layer of crisp gem lettuce. Place the bacon-fat-fried toast slice in the middle as the divider. Spread another light layer of mayo over the fried toast. Add a bit more lettuce, spoon over a small drizzle of the leftover tomato marinade juices, and top with the crispy bacon strips. Spread mayo onto the top bread slice and close the sandwich.
Press and Serve: Press down firmly on the sandwich so the juices and mayonnaise soak into the bread layers, making it easy and clean to eat. Slice in half and serve immediately.