Combine flax seed oil, lemon juice, lemon zest, balsamic vinegar or red wine vinegar, water, mustard seeds, Dijon mustard, tahini, sesame seeds, and pressed garlic cloves in a tight-lidded jar.

Chop fresh parsley and add to the jar.

Secure the lid tightly.

Shake the jar well until all ingredients are fully combined and emulsified.

Serve immediately or store in the refrigerator for up to a week.