1/2 to 1 tsp. Dijon-type mustard
2 tbsp. balsalmic vinegar
2 tbsp. fresh lemon juice
grated cheese to taste (I use a good-sized block)
3/4 cup cold-pressed extra virgin olive oil
1 egg + 1 egg yolk
2 cloves garlic, peeled and roughly chopped

Place all ingredients apart from the olive oil in a blender and blend until smooth. Gradually add the olive oil and allow the mixture to emulsify.

If you cannot eat cheese then this is still fab without it. You could try adding the 4 anchovy filets the original recipe calls for.