Preheat the oven to 350°. Spread the hazelnuts in a pie plate and toast for 12 minutes, or until fragrant and blistered. Rub the nuts in a kitchen towel to remove the skins. Finely grind the nuts in a food processor.
Wipe out the processor. Add the butter and sugar and process until fluffy. Add the egg yolk and vanilla and process until just blended. Add the flour, salt and the ground hazelnuts and pulse until a crumbly dough forms.
Scrape the dough into a large disk, then press the dough into a 9-inch fluted tart pan with a removable bottom. Line the dough with plastic wrap and press evenly into the pan. Freeze until firm, about 10 minutes.
Discard the plastic and press a piece of well-buttered foil directly onto the dough. Fill the foil with pie weights or dried beans and bake for 30 minutes, or until the shell is golden around the edge. Remove the foil and weights and bake for 15 minutes longer, or until golden all over. Let cool on a wire rack.
In a medium saucepan, bring the cream to a boil. Remove from the heat. In a medium bowl, whisk half of the warm cream with the egg yolks. Return the cream to the saucepan and whisk constantly over moderately low heat, until an instant-read thermometer registers 160°. Remove from the heat and immediately stir in the chocolate, butter and vanilla and whisk until smooth. Let the filling cool to room temperature.
In a medium bowl, toss the bananas with the sugar and rum. Arrange the bananas in a single overlapping layer in the tart shell and spoon the chocolate cream on top. Smooth the surface with a warmed offset spatula. Chill the tart until firm before serving.