In 2-quart saucepan, mix apples, brown sugar, 1 tablespoon of the water and the lemon juice. Cook over medium heat, stirring occasionally, until bubbly. Reduce heat to low; cover and cook 6 to 8 minutes, stirring occasionally, until apples are tender.
In small bowl, mix flour, granulated sugar and salt. Gradually stir into apple mixture, cooking and stirring until mixture thickens. Remove from heat; stir in butter and vanilla. Cool 15 minutes.
Meanwhile, heat oven to 375°F. Let pie crust pouch stand at room temperature for 15 minutes.
Remove pie crust from pouch; unroll crust on ungreased cookie sheet. Spoon cooled fruit mixture evenly onto half of crust to within 1/2 inch of edge.
In small bowl, beat egg and 1 tablespoon water; brush over edge of crust. Fold untopped half of crust over apple mixture; firmly press edge to seal. Flute edge; cut small slits in several places in top crust. Brush top with remaining egg mixture.
Bake 25 to 35 minutes or until crust is golden brown. Serve warm or cool.