Preparation

Make the chocolate dough

• Sift the flour and cocoa powder into a medium bowl.

  In a stand mixer fitted with the paddle attachment, cream the butter and sugar on medium speed until smooth, 3 to 4 minutes. Scrape the sides of the mixing bowl. Add the egg and beat well. In two batches, add the flour mixture and mix on medium-low speed until incorporated.

  Scrape the dough onto plastic wrap, shape into a flat square, and wrap well. Refrigerate the dough for at least 4 hours or overnight.

Make the pastry cream

• In a medium saucepan, heat the milk over medium-high heat until small bubbles form around the edges, about 3 minutes. Remove from the heat. In a medium bowl, whisk the yolks, sugar, cornstarch, rum, and vanilla seeds. Slowly whisk in the milk. Pour the mixture back into the pan and stir well. On medium heat, whisk until it boils and becomes thick and shiny, 3 to 4 minutes. Transfer to a stand mixer fitted with the paddle attachment. Add the butter and mix on medium speed until smooth, about 1 minute. Pass the cream through a fine sieve into a shallow bowl. Transfer to a disposable pastry bag. Squeeze it down to the tip and refrigerate until ready to use. (The pastry cream can be made up to 1 day ahead.)

Make the chocolate sauce

• Put the chocolate in a medium heatproof bowl. In a medium saucepan, heat the heavy cream, milk, corn syrup, and butter over medium heat. When steaming hot, pour the cream mixture over the chocolate and let sit for 5 minutes. Whisk until smooth. Set aside.

Bake the crusts

• Position a rack in the center of the oven and heat the oven to 350°F.

  Between two large sheets of parchment, roll the dough out into a 1/4-inch-thick rectangle that’s about 13-1/2×10 inches. Slide it onto a rimmed baking sheet and freeze. Once the dough is firm, after about 30 minutes, trim to 12-1/2×9 inches and then cut it into ten 2-1/2×4-1/2-inch rectangles. Arrange on a rimmed baking sheet and bake until set and dry, 10 to 15 minutes, rotating the pan after 5 minutes. Cool completely on the baking sheet on a rack.

Whip the cream

• In a stand mixer fitted with the whisk attachment, beat the cream on medium speed until it starts to thicken, about 2 minutes. Add the sugar and continue to beat until soft peaks form, about 1 minute. Add the vanilla and switch to a hand whisk, whipping until the cream forms stiff peaks.

Assemble the tarts

• In a small saucepan, gently warm the chocolate sauce over low heat.

  Cut a 1/2-inch hole at the tip of the bag of pastry cream. Pipe the cream in a zigzag pattern across each tart crust to cover completely.

  Peel and cut the bananas into 2-1/2-inch lengths, then slice them lengthwise 1/8 inch thick. Shingle the bananas across the pastry cream. Sprinkle each tart with 1 tsp. turbinado sugar. Pass the flame of a small kitchen torch over the bananas until the sugar bubbles and caramelizes. Let cool briefly.

  Transfer the whipped cream to another pastry bag, fitted with a star tip, and pipe a string of 1/2-inch rosettes down one long side of each tart over the bananas. Dust with cocoa powder. Garnish with mint leaves (if using).
  Serve the tarts with a scoop of ice cream on the side. Pour the warm chocolate sauce over the tart at the table.