Chill your glasses. Place two coupe or martini glasses in the freezer for at least 10 minutes.
Prepare the mixing glass. Add plenty of ice to a mixing glass.
Add the whiskey and vermouth. Pour in the bourbon or rye, then the sweet vermouth.
Add the bitters. Drop in several dashes of Angostura bitters.
Stir gently. Stir for 20 to 30 seconds until the mixture is very cold.
Strain and serve. Remove the chilled glasses from the freezer and strain the cocktail evenly between them.
Garnish. Add a cherry to each glass and run an orange peel over the rim if desired.