Form ground beef into 4 patties about 3/4- to 1-inch thick.
Press coarse black pepper into both sides to taste.
Place patties on a plate, cover and place in the refrigerator.
Combine red wine and mustard in a saucepan and place over medium heat on the stove.
If using dried tarragon, add it now.
Simmer until reduced by half.
Add the green peppercorns and cream and simmer until liquid becomes saucelike.
Remove from the heat and add fresh tarragon.
Place a large, heavy skillet on the stove over high heat.
When it is nearly smoking, add the hamburger patties.
Cook 2 minutes.
Turn the patties and cook on the other side until desired doneness, about 1 minute for very rare, 4 minutes for medium-well.
To serve, arrange a burger on a toasted bun bottom and generously spoon some sauce over the top.
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