Peel bananas and cut crosswise into thirds.

Stir together beignet mix, water, and coconut milk until mixture forms a soft dough. Add additional mix or water to adjust texture to that of a soft biscuit dough. Do not overmix.

Turn out dough onto a lightly floured surface and roll 1/8-inch thick, sprinkling with additional flour as necessary. Cut dough into rectangles to fit the banana pieces. Wrap bananas in dough and pinch seams closed.

Heat oil to 370º in a deep fryer or deep pot. Fry the beignets in the oil, a few at a time, until puffed and golden brown on all sides. Remove to a rack set over a cookie sheet to drain. If there is additional beignet dough remaining, it can be fried now. Do not reroll dough scraps as they will toughen.

Place fried beignets in a saute pan over medium heat and sprinkle with sugar. Pour warm rum over the beignets and carefully ignite with a long match (or a steady hand!). Saute gently until the flames are out. Serve beignets immediately with rum sauce and sesame seeds.