1. Mix the cold milk, lemon juice, garlic, and white pepper in a blender. Whiz on high speed for thirty seconds, until light and frothy. If using a hand blender, make the mayonnaise in a tall glass measuring cup.
2. With the blender on high speed, very slowly begin to drizzle in the oil, drop by drop, until it begins to thicken and become emulsified.
3. Continue to add the oil, in a very thin stream, until the mayonnaise is thick and smooth. Do not try to make this too quickly; the process of slowing incorporating the oil should take several minutes.
4. Finely chop the chervil leaves and add them to the mayonnaise, along with the salt. Taste, adding more salt and lemon juice, if desired.
Serve the sauce at room temperature. The sauce can be refrigerated for up to one week.