Preheat oven to 350°. Unfold phyllo sheets on a flat work surface. Stack 5 phyllo sheets, brushing each sheet with 1 Tbsp. melted butter and sprinkling with 1 tsp. sugar. Cut into 12 squares, and transfer to a parchment paper-lined jelly-roll pan, spacing them about 1 inch apart.
Bake at 350° for 14 minutes or until golden brown and crispy.
Combine berries, 1 Tbsp. sugar, and lime zest.
Beat cream and buttermilk at high speed with an electric mixer until foamy; gradually add remaining 11⁄2 Tbsp. sugar, beating until stiff peaks form.
Place 6 phyllo squares on individual serving plates; top each with 11⁄2 Tbsp. whipped cream and 3 Tbsp. berry mixture. Top each with another phyllo square and equal portions of the remaining whipped cream and berries.
Garnish, if desired, and serve immediately.