Smash up the garlic with sea salt using a pestle and mortar (or use the end of a rolling pin and a small bowl).
Place egg yolk and mustard in a medium bowl. Whisk until blended. Start adding oil, bit by bit, stirring vigorously till creamy. Make sure to blend well each time you add a bit of oil into the egg yolk mixture.
When all the oil has gone in and the mixture is thickened, add lemon juice and the smashed garlic with salt. Mix well. Stir in the parsley if using until evenly mixed. Taste, season with more salt, pepper, or lemon juice if needed.
Store in an air-tight container in the fridge for up to 5 days.