Finely mince the shallot (use two if they're smaller. You want about a quarter cup) and the fresh tarragon.
Place the shallots, tarragon, vinegar and wine in a sauce pan.
Reduce until the liquid is almost totally evaporated.
Remove from heat, and stir in butter, a chunk at a time. You want to cream the butter, but not truly melt the butter, so keep stirring the sauce.
Continue adding butter ...
... until you have sufficient sauce.
Strain the sauce through a fine sieve, pressing on solids to extract everything.