In a heavy, medium saucepan, bring the milk to a simmer over medium-low heat.
In a large bowl, whisk the egg yolks until pale yellow. In a small bowl, combine the sugar, flour and salt. Gradually add the sugar mixture to the yolks, whisking until smooth. Pour about a quarter of the hot milk into the yolk mixture, whisking constantly to prevent scrambling, then whisk into the remaining milk. Add the vanilla extract and, whisking constantly, bring to a boil. Cook, whisking vigorously, for 2 minutes. Remove from the heat, stir in the butter and whisk until smooth. Pour into a greased medium bowl, cover with plastic wrap and refrigerate until cool and firm to the touch, at least 2 hours.
In a medium bowl, mash the bananas until smooth. Stir into the cooled custard.
Line a medium baking dish with wax paper. In a medium saucepan, heat the oil over medium-high heat until rippling. Add the chocolate chips, remove from the heat and beat with a spoon until melted and smooth. Working with 4 cones at a time, fill each cone with melted chocolate; let stand for 1 minute, then pour the extra chocolate back into the saucepan, leaving a thin coating in each cone. Place all the chocolate-lined cones upside down in the prepared baking dish for a few minutes to drain, then freeze until the chocolate is firm, about 10 minutes.
Spoon the banana custard into each cone, forming a small mound at the top. Refrigerate until the filling is firm, at least 1 hour. Top with whipped cream and serve cold.