PLACE the egg, 1/4 cup of olive oil, mustard powder, and salt in a mixing bowl, blender, or food processor. Mix thoroughly.
WHILE the food processor or blender is running (or while mixing in a bowl with a stick blender), slowly drizzle in the remaining cup of olive oil.
AFTER you’ve added all the oil and the mixture has emulsified, add lemon juice to taste, stirring gently with a spoon to incorporate.