Peel and cut into thin slices, 1–2 mm, using a mandoline or a knife
Melt the butter and stir in the salt
Preheat the oven to 150°C (300°F)
In a loaf pan lined with parchment paper, arrange a layer of potato slices, overlapping each slice by one third
Using a pastry brush, brush with butter and sprinkle with pepper. Repeat until all the potatoes are used up.
Cover the top of the pan with aluminum foil and bake for 1 hour 30 minutes, until the potatoes are tender (the blade of a knife should slide in easily)
Remove from the oven, let cool slightly, then place a weight on top and refrigerate overnight.
The next day, unmold by turning the pan upside down, then cut into individual portions
In a hot pan lined with parchment paper, add a little oil and brown the potato squares on each side
Preheat the oven to 220°C (425°F) and roast the peppers until blackened, about 15 minutes on each side
Let them cool slightly, then remove the skin that will peel off easily, along with the seeds and the white membranes inside
Blend until smooth
In a saucepan, add 220 g of this mixture along with the remaining ingredients except the cornstarch, and heat over low heat
Mix the cornstarch with 1 tablespoon of water to form a paste, then add it to the saucepan. Cook for 5 minutes, until the sauce thickens, then let cool
In boiling water, blanch the basil leaves for 30 seconds, reserving 2 leaves
Immediately transfer them to a bowl of ice water to stop the cooking and set the color, then drain, pressing the leaves to remove excess water
Blend with the oil until smooth
In a narrow bowl, add the egg yolk, mustard, lemon juice and salt
Make the mayonnaise using an hand blender or a whisk, slowly drizzling in the green oil
Add the 2 reserved basil leaves and blend until fully incorporated