Step 1Combine the mustard and vinegar in a blender and blend at medium speed for about 15 seconds. With the machine running, slowly drizzle in one-half cup of the oil. Don't be tempted to add all the oil to the blender or the vinaigrette will become too thick. It should be very creamy.
Step 2Transfer the vinaigrette to a small bowl and, whisking constantly, slowly stream in the remaining 1 cup oil. (The dressing can be refrigerated for up to 2 weeks. Should the vinaigrette separate, use a blender or immersion blender to re-emulsify it.)