Peel and devein shrimp, leaving tails on, if desired. Combine 1/2 cup wine, broth, and 2 dillweed sprigs in a medium saucepan. Bring to a boil; add shrimp, and cook 3 to 4 minutes or until shrimp turn pink. Transfer shrimp and liquid to a bowl. Cover and chill thoroughly.
Cut bread slices into 12 rounds with a 2-inch biscuit cutter. Reserve remaining bread pieces for another use. Place bread rounds on a baking sheet. Broil 5 1/2 inches from heat (with electric oven door partially opened) 1 minute on each side or until lightly toasted.
Combine cream cheese, minced dillweed, and remaining 1 teaspoon wine. Spread cheese mixture evenly over one side of bread rounds. Remove shrimp from liquid; discard liquid. Place one shrimp on each bread round. Garnish with fresh dillweed sprigs, if desired.