Add egg yolk, lemon juice, mustard, salt and water to a medium bowl and whisk until thoroughly combined.
Whisking constantly (you can use the whisk attachment in your immersion blender!), drizzle in a few drops of your oil at a time. Your mixture should be opaque, with all the oil incorporating into the mixture. Once your mixture emulsifies (i.e. begins to thicken), you can increase the speed of oil a tad into a small stream rather than drop by drop. Keep whisking and adding in the oil until a rich and thick mayo emerges (always best to go slower the first time around!).
Keep stored in the fridge, in an airtight container, for about 3-4 days.
Notes
Please note that one batch yields about 1 cup (i.e. 16 tablespoons!).