Bring all the ingredients at room temperature: the egg yolk, gastrique, mustard and oil in particular
Separate an egg yolk from the white and use the yolk and place in a sufficiently large bowl
Add 4 teaspoons of Dijon mustard and optionally a pinch of xanthan gum and mix with the whisk
Add one teaspoon of the gastrique, the salt, pepper and the soy sauce and mix
Measure 1.5 cup of the tarragon infused oil
Whisk in the oil, first drop by drop, later in a slightly larger stream, while mixing vigorously. The mixture will become more and more viscous
Keep whisking and when about half of the oil is added, add some fresh lemon juice and the honey and whisk in. The emulsion will become slightly thinner and a little more whitish. Then continue to ehik in more oil, until the mixture becomes really viscous
if so desired, add more fresh lemon juice (use drops), salt or honey to taste and keep mixing. Add a bit more oil to bring the viscosity back up, if needed.
Place the mayonnaise in a glass jar and store in the refrigerator to let the flavors blend in. Store for a few weeks.