Stir together yogurt and honey; cover and chill yogurt sauce until ready to serve.
Combine strawberries and 2 Tbsp. sugar; cover and chill until ready to serve.
Place 1 phyllo sheet on a flat work surface. Coat with cooking spray, and sprinkle evenly with 1/4 tsp. sugar. Top with 1 phyllo sheet; coat again with cooking spray, and sprinkle with 1/4 tsp. sugar. Cut phyllo stack into thirds lengthwise; cut each in half, creating 6 even rectangular stacks. Repeat procedure with remaining phyllo sheets, cooking spray, and 1/2 tsp. sugar.
Grill phyllo stacks, without grill lid, over medium-low heat (300° to 350°) 1 to 2 minutes on each side or until lightly browned.
Place 1 grilled phyllo stack on each of 6 serving plates; top evenly with half of strawberry slices. Drizzle evenly with half of yogurt sauce. Top each with 1 grilled phyllo stack. Top evenly with remaining strawberry slices and yogurt sauce. Garnish, if desired. Serve immediately.