Melt butter in saute pan. Add the sugar, spices, honey and rum. Let simmer over medium heat for 5 minutes or until it reaches the consistency of maple syrup.
Add sliced bananas to the sauce mixture. Cook for 1 1/2 minutes more, or until bananas become slightly soft. Remove pan from heat and pour the entire contents through a strainer. Remove bananas from the strainer and put them into the refrigerator to cool. Reserve sauce in another container.
After bananas have cooled, mix together the egg and milk in a bowl. Lay out the flour tortillas. Place 1/4 of the banana mixture in the center of the tortilla, leaving about 3/4-inch around the edge of the tortilla. With a brush or your hand, rub the remaining area of the tortilla with an egg wash. Fold the sides of the tortilla toward the middle.
Take the end of the tortilla closest to you and roll over the banana mixture until the tortilla is closed like a burrito.
Heat oil in a pan until it reaches 350-375°. Lay the burrito in the hot oil in the pan and fry until golden brown. Remove and place on a towel. Slice diagonally with a serrated knife and serve with the remainder of the sauce and ice cream.