Add all the ingredients to a small saucepan, or reduction pan.
Bring to a simmer, over medium-low heat.
Allow the pan to reduce until you have about 2 tablespoons of thick liquid, about 15 to 20 minutes.
Chef’s Note: In the last few minutes, keep a close eye on the pan so that it doesn’t go dry.
Remove the thyme, and bay leaf, and then allow to cool.
Gather your ingredients.
Add the cooled shallot reduction, butter, and egg yolks into a cold saucepan.
Place over low heat, and begin whisking.
After the butter completely incorporates into the other ingredients, turn the heat up a bit, and continue to whisk, as the sauce thickens, about 3 to 5 minutes.
Chef’s Note: If the sauce gets too hot, it will begin to cook the eggs, and curdle… If you see any steam coming off the sauce, remove it from the heat, and keep whisking, then return the pan to the heat until it thickens, and leaves trails when you drag the whisk over the bottom of the saucepan.
Remove from the heat, and then add some lemon juice, and pepper, to taste.
Chef's Note: Serve while still warm, or keep warm over a water bath (bain-marie), until needed.
Ladle it over some chicken, beef, or pork, and serve with your favorite starch… like a big plate of garlic mash potatoes. Enjoy.