In a small saucepan, combine the white wine vinegar, dry white wine, minced shallots, 1 tsp chopped tarragon (and any reserved stems), and crushed black peppercorns. Bring the mixture to a simmer over medium heat and reduce until about 2 tablespoons of liquid remain. This should take about 5-7 minutes. Strain the reduction through a fine-mesh sieve into a heatproof bowl, pressing on the solids to extract all liquid. Discard the solids.

Fill the bottom of a saucepan with about 1-2 inches of water and bring it to a gentle simmer. Place the heatproof bowl containing the strained reduction over the simmering water, ensuring the bottom of the bowl does not touch the water.

Add the 3 egg yolks to the bowl with the reduction. Immediately begin whisking vigorously and constantly. Continue whisking for 3-5 minutes, or until the mixture thickens, lightens in color, and forms ribbons when the whisk is lifted. This process is crucial for cooking the egg yolks without scrambling them.

Remove the bowl from the heat (or keep it over very low heat, continuing to whisk). Slowly, in a very thin, steady stream, begin to whisk in the warm melted butter. Pour very gradually at first, ensuring the sauce emulsifies properly. Continue whisking constantly as you add the rest of the butter. If the sauce becomes too thick, you can add a tiny splash of warm water.

Once all the butter is incorporated and the sauce is thick and smooth, whisk in the heavy cream. Stir in the 1 tbsp finely chopped fresh tarragon, a pinch of salt, and a pinch of white or black pepper. Taste and adjust seasonings as needed.

Serve your Creamy Bernaise Sauce immediately with grilled steak, poached eggs, asparagus, or roasted chicken.