Preheat oven to 425ºF. Line a baking sheet with parchment paper. Combine sugar and cinnamon in small bowl.
Place 1 phyllo sheet on parchment with short side facing you; cover remaining sheets with a damp kitchen towel. Brush with butter, sprinkle with cinnamon sugar and walnuts. Lay second sheet of phyllo on top, brushing with butter and adding cinnamon sugar and walnuts. Repeat with remaining 2 phyllo sheets.
Lay bananas horizontally on lower third of phyllo, leaving a 1-inch border on sides and bottom, trimming bananas if necessary. Sprinkle chocolate chips over bananas. Fold long sides of phyllo toward center, over ends of bananas. Fold bottom edge over bananas. Roll up bananas in phyllo, away from you.
Position strudel, seam side down, in center of baking sheet. Beat egg with 1 Tbsp. water and brush egg mixture over strudel. Use a serrated knife to cut 4 vents in dough. Bake until golden brown, about 15 minutes.