In a medium bowl, gently stir water, egg yolks and lemon juice until no streaks of yolk remain. Microwave the mixture stirring gently every 10 seconds until the mixture thickens slightly, 1 to 2 minutes. Remove from the microwave and immediately add 1/4 cup oil, salt. mustard and sugar and whisk to combine.

Strain the mixture through a fine mesh strainer into a food processor. With the food processor running, slowly drizzle in the remaining 1 1/4 cups oil in a thin stream about 2 minutes. Scrape the bottom and sides of the bowl and process 5 seconds longer.

Transfer to an airtight container and refrigerate for up to 1 month.