Béarnaise Mayonnaise

1 fl oz (30 mL) white wine vinegar, 1½ fl oz (45 mL) white wine, 2 tsp (10 mL) minced shallot, 1 tsp (5 mL) dried tarragon, (all reduced to 1½ fl oz (45 mL) and cooled), ½ oz (15 g) minced fresh tarragon leaves