In a small saucepan, bring 6 Tbs. of brown sugar and the butter and water to a boil. Stir in liquor; simmer to blend flavors, about 1 minute. Remove from heat, and set aside.
Place one flour tortilla on a work surface. Place 1?3 of the banana slices just below the center, forming the fruit into a log; sprinkle with 1 Tb. brown sugar and 1 Tb. walnuts. Fold both sides of the tortilla over the filling, then fold bottom of the tortilla over the filling and roll it over to form a packet. Secure with toothpicks. Repeat with remaining tortillas, bananas, sugar and nuts. (You can make ahead to this point and hold at room temperature for 1 hour.)
Meanwhile, warm oil in a Dutch oven set over medium heat until it reaches 350 degrees on a candy or deep-fry thermometer. Add all three stuffed tortillas. Fry, turning once, until golden brown, about 2 minutes on each side.
Transfer to paper towels, lightly blot surface oil, remove toothpicks and halve on the diagonal with a serrated knife.
Spoon 1 Tb. butter sauce in the bottom of each of six shallow bowls. Place half a tortilla and 1?2 cup of ice cream in each pool of sauce. Drizzle with remaining sauce, and serve immediately.
