aioli

1. In a small heatproof bowl, place whole egg and cover with boiling water. Let sit for 1 minute to minimize bacteria on the shell and begin to cook the proteins, which will help with the emulsification. Separate the egg, place the yolk in a clean bowl and discard the white.
2. Using a handheld mixer with a whisk attachment, break up the yolk and whisk until smooth. Alternatively, use a handheld whisk.
3. Combine oils in a glass measuring cup or plastic squeeze bottle, if available, to allow for slow and controlled pouring. With the mixer running, start adding the oils very slowly, a few drops at a time, and eventually progressing to a slow, fine stream. Every now and then, stop adding oil completely and whisk the mixture to ensure it is fully emulsified. If you accidentally add too much oil at once, whisk rapidly for a few seconds to combine and then proceed with more oil in a slow, steady, very patient manner. After about 1/2 cup oil has been added, the aioli may have a stringy or taffy-like appearance which indicates the egg yolk is reaching saturation (or a "tight" emulsion). At this point, whisk in 1/2 tsp of diluted lemon juice to loosen the mixture. Continue adding more oil, whisking constantly, until the tightness reappears, then add a scant 1 tsp diluted lemon juice and the garlic paste. Continue this process of slowly whisking in the oil and adding the diluted lemon juice when tight until all the oil and lemon juice have been added.
4. Stir in the salt, adjusting amount to taste, cover with plastic wrap and refrigerate for up to 2 days.

dressing

1. Preheat oven to 325°F.
2. In a small bowl, cover shallot with vinegar and 1/2 tsp salt, and macerate for 10 minutes.
3. Spread the pistachios on a small baking sheet and bake until lightly toasted, 3 to 4 minutes. Cool, roughly chop and divide into two groups of 1/2 cup and 1/4 cup, and set aside.
4. Whisk together macerated shallot and its soaking vinegar, remaining 3/4 tsp salt, lemon zest and juice, the aioli, olive oil and creme fraiche (or sour cream if substituting). Whisk in the herbs and 1/2 cup of chopped pistachios, taste, and adjust seasoning as needed.

salad

1. Trim off the brown end of the base of each lettuce, but leave the head intact. Peel off old, outer leaves and cut each lettuce in half vertically. Wash lettuce by submerging heads in water, dry in a salad spinner, and set aside.
2. Slice radishes to the thickness of a dime, using a mandoline or a sharp knife, and submerge in a small bowl of ice water. About 5 minutes before serving, remove the radishes from the water and dry well in a salad spinner.
3. To serve family style, put about 2/3 cup of the vinaigrette on a serving plate and arrange the lettuce halves on top. Spoon the remainder of the vinaigrette over the top of the lettuce. Top with the radish slices, the remaining chopped pistachios, a sprinkle of finishing salt, and freshly ground black pepper.