To prepare pastry, lightly spoon flour into dry measuring cups; level with a knife. Combine flour, cream cheese, butter, and 1 teaspoon salt in a 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.
To prepare filling, 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; cook 1 minute or until soft. Stir in mushrooms, 1/8 teaspoon salt, and pepper. Cook 10 minutes or until most of liquid evaporates, stirring frequently. Remove from heat; stir in basil. Cool completely.
Preheat oven to 350°.
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. Working with 1 portion at a time, roll each dough ball into a 4-inch circle on a lightly floured surface. Lightly brush pastry with egg white mixture. Spoon about 2 teaspoons mushroom 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 on a baking sheet lined with parchment paper. Repeat procedure with remaining dough, filling, and egg white mixture, placing pastries 1 inch apart.
Bake at 350° for 20 minutes or until lightly browned. Let stand 5 minutes before serving.