Combine flour, cream cheese, butter, and 1 teaspoon salt in food processor, pulse 4 times or until mixture resembles coarse meal. With processor on, add ice water through food chute, processing until dough forms a ball. Gently press mixture into a 4-inch circle on plastic wrap. Cover and chill 15 minutes or up to 1 day.
Place mushrooms in food processor, and process until finely chopped. Heat a large nonstick skillet coated with cooking spray over medium-high heat. Add shallots and butter; cook 1 minute or until soft. Stir in mushrooms, salt and pepper. Cook 10 minutes or until most of liquid evaporates, stirring frequently. Remove from heat, stir in basil or thyme. Cool completely. Can be made one day ahead.
Combine 2 teaspoons water and egg white in a small bowl, stir well with a whisk.
Divide dough into 24 equal portions. Shape each portion into a ball, chill. Roll each dough ball into a 4-inch circle on a lightly floured surface. Lightly brush pastry with egg white mixture. Spoon about 2 teaspoon smushroom filling onto half of each circle. Fold dough over filling; press edges together with a fork to seal. Brush egg white mixture over pastry. Place ona baking sheet lined with parchment paper. Repeat procedure with remaining dough, filling, and egg white mixture, placing pastries 1 inch apart.
Bake at 350 degrees for 20 minutes or until lightly browned. 24 servings.