Preheat oven to 425°.
Roll each dough portion into a 12-inch circle on a lightly floured surface. Cut the dough into 36 circles with a 2 1/2-inch round cutter. Press 1 dough circle into each of 36 miniature muffin cups. Press into the bottoms and up the sides of muffin cups. Bake at 425° for 7 minutes or until lightly browned. Remove from pans; cool on wire racks.
Combine apricots and next 4 ingredients (apricots through juice) in a small saucepan; bring to a boil. Reduce heat; simmer 10 minutes or until liquid is absorbed. Stir in honey and remaining ingredients. Cool. Spoon about 2 teaspoons apricot mixture into each pastry shell.