In a large saucepan, over medium-high heat, bring the wine, onion, pepper, and whole tarragon sprigs to a boil. Reduce heat and simmer, uncovered, until the mixture is reduced by two-thirds, 20 to 25 minutes, depending on size of pan.
Remove and discard the tarragon sprigs. Add the cream, reduce heat, and simmer gently until slightly thickened, about 15 minutes.
Remove from heat and stir in the salt and chopped tarragon. Serve over chicken, fish, or vegetables.