Heat oven to 375°F. Spray 13x9-inch pan with cooking spray. In large microwavable bowl, beat eggs. Reserve about 2 tablespoons beaten egg; set aside.
Add carrot, bouillon, chives, salt, water and milk to eggs in bowl; mix well. Microwave uncovered on High about 2 1/2 minutes or just until hot. Add potato flakes; mix well.
If using crescent rolls: Unroll dough into 2 long rectangles. Overlap long sides to form large rectangle. Firmly press perforations and edges to seal. Press to form 14x10-inch rectangle. If using dough sheet: Unroll dough. Press to form 14x10-inch rectangle.
Spread potato mixture over dough. Sprinkle with cheese. Starting with long side, roll up dough; seal long edge. Cut crosswise into 8 slices. Place cut side down in pan; press each to flatten slightly. Brush each with reserved beaten egg.
Bake 25 to 30 minutes or until golden brown. Cool in pan 3 minutes. Remove from pan. Serve warm.