Chop the shallot and tarragon and add to wine and champagne vinegar in a saucepan, cook until reduced to ¼ cup of liquid
Add ¼ of liquid and 1tbsp of the cooked shallots and tarragon to the top of a double boiler over simmering water, be careful to not allow the bottom of the bowl to touch the water
Add the egg yolks and whisk continually until the eggs start to thicken
Remove pan of water from heat and add some ice cubes to cool the simmering water
Return bowl to the double boiler and start slowly adding the butter while whisking continuously, continue until all of the butter is incorporated. If the sauce starts to break, remove the bowl from the double boiler and continue whisking.
Once all butter is incorporated add the salt pepper and cayenne
Recipe by Only From Scratch at https://www.onlyfromscratch.com/bearnaise-sauce-recipe/