1. Combine vinegar, shallot, mayonnaise, mustard, salt, and pepper to taste in small nonreactive bowl. Whisk until mixture is milky in appearance and no lumps of mayonnaise remain.

2. Place oil in small measuring cup so that it is easy to pour. Whisking constantly, very slowly drizzle both oils into vinegar mixture. If pools of oil are gathering on surface as you whisk, stop addition of oil and whisk mixture well to combine, then resume whisking in oil in slow stream. Vinaigrette should be glossy and lightly thickened, with no pools of oil on its surface.

Makes about 1/4 cup, enough to dress 8 to 10 cups lightly packed greens