Heat oven to 350°F. Spray six 6-oz. custard cups or ramekins with nonstick cooking spray. Place cups in ungreased shallow baking pan. Place 1 pastry sheet on work surface. Brush lightly with butter. Place second sheet on top. Continue brushing with butter and stacking with remaining 2 pastry sheets. Sprinkle top of stack with lemon-pepper seasoning.
Cut stack in half crosswise to make two 14x9-inch rectangular stacks. Place 1 stack on top of the other. With pizza cutter or sharp knife, cut stack lengthwise in half. Cut each half into 3 equal pieces to make a total of 6 stacks, each about 4 1/2x4 1/2 inches. Press 1 stack into each sprayed custard cup.
Break 1 egg into each pastry-lined cup. Sprinkle eggs with salt and pepper. Bake at 350°F. for 18 to 20 minutes or until pastry baskets are golden brown and crisp, and eggs are just about set.
Meanwhile, place spinach in microwave-safe dish; cover. Microwave on HIGH for 1 to 1 1/2 minutes or until hot. Stir in mayonnaise.
Remove pan with cups from oven. Top each egg with about 2 tablespoons spinach mixture. Sprinkle with cheese.
Return to oven; bake an additional 3 to 5 minutes or until spinach mixture is thoroughly heated. Carefully, slide egg baskets from custard cups onto serving plates.