Preheat oven to 375°F. Mix cream cheese, 1/4 teaspoon of the dill and ginger in small bowl. Stir in green onion. Set aside.
Unroll crescent dough; separate into 8 triangles. Cut each triangle in half to make 16 triangles. Stretch dough slightly and place crescent triangles into standard-size muffin pans so that the bottom of the muffin cup is covered and crescent corners are lying outside the cup.
Divide shrimp evenly into cups (about 1 heaping teaspoon per cup). Top each cup with 1/2 teaspoon of the cream cheese mixture. Loosely fold dough corners into center; pinch corners together and twist to seal tightly. Lightly sprinkle tops with remaining 1/4 teaspoon dill.
Bake 15 to 17 minutes or until crisp and golden brown.