Process yolks, mustard, lemon juice, and garlic in food processor until combined, about 10 seconds. With machine running, slowly drizzle in vegetable oil, about 1 minute. Transfer mixture to medium bowl and whisk in water. Whisking constantly, slowly drizzle in olive oil, about 30 seconds. Whisk in salt and pepper. Refrigerate in airtight container for up to 4 days.

Makes about 1 1/4 cups