Bananas Foster Mille-Feuille

Preheat oven to 375°. Line one baking sheet with parchment, leave a second baking sheet unlined, and set aside another sheet of parchment.

Warm ghee in microwave just until liquefied (but not hot). Unroll phyllo sheets; cover with plastic wrap and a damp towel.

Place one phyllo sheet on lined baking sheet and brush with ghee; repeat with remaining sheets and ghee.

Cut phyllo stack into fourths, crosswise (about 3½×9 inches). Halve each rectangle, crosswise, to make squares (about 3½×4½ ), then cut each square diagonally to form triangles; evenly space triangles on same baking sheet.

Bake triangles until beginning to puff, 4 minutes. Top triangles with reserved parchment, followed by unlined baking sheet, pressing to flatten triangles. Bake triangles until browned, 4 minutes more. Remove top baking sheet and parchment; let triangles cool to room temperature.

Combine powdered sugar, mascarpone, and 1 Tbsp. cream with a mixer until smooth; chill until ready to use.

Melt 4 Tbsp. butter with brown sugar, liqueur, rum, 1 Tbsp. cream, and corn syrup in a skillet over medium-high heat. Bring caramel mixture to a boil, then reduce heat to medium and simmer until thickened, whisking often, 2–3 minutes. Transfer caramel to a heat-proof bowl to cool.

Pour 1 Tbsp. caramel on a serving plate; top with a phyllo triangle, 2 Tbsp. mascarpone mixture, sliced bananas, and strawberries. Carefully arrange a second phyllo triangle on top of strawberries; top with 2 Tbsp. mascarpone mixture, sliced bananas and strawberries. Carefully arrange a third (final) phyllo triangle on top of strawberries; top with 1 Tbsp. mascarpone mixture and banana chips. Drizzle 2–3 Tbsp. caramel on Mille-Feuille. Repeat assembly with remaining caramel, phyllo triangles (less one extra), mascarpone mixture, bananas, strawberries, and banana chips.