Preheat oven to 400F. For filling, in a medium skillet, cook lamb or beef and onion over medium-high heat until brown. Remove from heat. Drain off fat. Add spinach, cheese, milk, lemon peel, salt, and the 1/4 teaspoon nutmeg to meat mixture; stir until combined. Set aside.

Unfold phyllo dough; remove one sheet. (While you work, keep the remaining phyllo dough covered with plastic wrap to prevent it from drying out.) Brush with some of the melted butter. Top with another sheet of the phyllo, matching edges and corners; brush with butter. Repeat with remaining phyllo, brushing each layer with some of the butter.

Using a sharp knife, cut the phyllo stack in half crosswise. Spread half of the filling lengthwise on each phyllo piece. (Spread filling within 2 inches of the long edges and 1-1/2 inches of the short edges.) Fold each packet: Fold short phyllo sides over filling. Fold a long phyllo side over filling, then fold several times to encase filling.

Place phyllo packets, seam sides down, on a baking sheet. Brush with any remaining melted butter; sprinkle with additional nutmeg. Diagonally score the tops of the phyllo packets, making cuts 1 inch apart and 1/4 inch deep. (Do not cut completely through the phyllo layers.)

Bake for 15 to 18 minutes or until golden. Let stand for 15 minutes before serving. To serve, slice phyllo packets along scored lines. Makes 16 to 20 appetizer servings.

To make ahead: Prepare as directed through Step 4. Wrap phyllo packets in moisture- and vaporproof wrap. Freeze for up to 3 months. To serve, preheat oven to 400F. Place frozen packets, seam sides down, on a large baking sheet; bake for 25 to 30 minutes or until golden. Let stand for 15 minutes before serving. To serve, slice phyllo packet along scored lines.