Combine cabbage and salt in a large bowl; toss well. Let stand 1 hour. Drain well. Pat cabbage dry with a paper towel. Return to bowl; set aside.
Heat oil in a large nonstick skillet over medium heat. Add onion; sauté 4 minutes. Stir in carrot; cover, reduce heat to low, and cook 8 minutes. Add lamb, cilantro, and garlic; cook, uncovered, over medium-high heat until browned, stirring to crumble. Drain lamb mixture in a colander; pat dry with paper towels. Add lamb mixture and sour cream to cabbage; toss well.
Preheat oven to 350°.
Divide dough into 30 equal portions. Working with 1 portion at a time (cover remaining portions to keep dough from drying out), roll into a 4-inch circle on a lightly floured surface. Spoon 2 heaping tablespoons cabbage mixture onto half of circle. Fold dough over filling; press edges together with a fork to seal. Place turnovers on a baking sheet coated with cooking spray, and brush with egg white. Repeat procedure with remaining dough, cabbage mixture, and egg white.
Bake at 350° for 25 minutes or until golden. Serve warm.