If Making Mayo:
Start by whisking the egg yolk, mustard, and a pinch of salt in a medium bowl until you get a very smooth mixture. You can stabilize the bowl by putting it inside a saucepan with a towel at the bottom. This will free up one hand for pouring and the other for whisking.
Combine the olive and vegetable oils in a measuring glass. Slowly pour the oil into the yolk mixture, beginning with a few drops and then adding more in a continuous stream as the mixture becomes thicker.
Add vinegar and hot sauce and whisk well; season with salt and pepper to taste. If the mayo is too thick, add water by the teaspoon until it reaches a spoonable consistency.
For the Eggs:
Bring a large saucepan of water to a boil, then carefully add the eggs. Keep the water simmering and cook the eggs for 7-9 minutes.
Use a slotted spoon to transfer the eggs to a bowl of ice water and stir them until they are cool enough to handle, about 1 minute. Drain the water, dry the eggs, and peel them.
Break the eggs into large pieces and mix them with mayonnaise. Season with salt and pepper to taste. Serve on bread.
In a small bowl, combine scallions, basil, dill, chives, and lemon zest. Drizzle oil over the mixture and add lemon juice and salt. Toss everything well. Top the egg with the herb salad.