Stir together flour and salt; cut in butter with a pastry blender until crumbly. Stir in cottage cheese until blended. Shape mixture into 1-inch balls. Cover and chill 8 hours.
Bring apricots and 1/2 cup water to a boil in a saucepan; cover, reduce heat, and simmer 15 minutes. Remove from heat; cool 10 minutes.
Process apricot mixture and 1/2 cup sugar in a food processor until smooth, stopping to scrape sides.
Pat each ball on a lightly floured surface into a 2 1/2-inch circle. Spoon 1 teaspoon apricot mixture in center of each circle. Fold circles in half, pressing edges to seal. Place on lightly greased baking sheets. Brush with egg white. Stir together remaining 1/2 cup sugar and almonds; sprinkle evenly over crescents.
Bake at 375° for 12 to 15 minutes or until lightly browned.