I didn't know the answer to the title question until this week, when I came across a recipe for it on the Huffington Post food page. This page supposedly includes every pie recipe you will ever need, and if you are a banana lover you can make this dessert for a special occasion and get raves.
The word "banoffee" is a combination of banana and toffee, and it features the use of toffee chips and sliced bananas in a pudding to fill a sweet crumb crust. The toffee chips are used in this crust, which will give it a lovely flavor but also a tendency to stick to the baking pan. For this reason I would use a heavy nonstick round baking pan or a spring-form pan such as the products marketed by Nordic Ware. I mean, that sturdy and that powerful a nonstick coating.
If you are into Southern cooking, you could well say that this pie is an amped-up version of Banana Cream Pie, with its addition of the toffee bits that are sold by the company that markets Heath Bars, among others. Personally, I don't like the combination of chocolate and fruit very much, and for that reason I would just pick up a package of Heath toffee bits without the milk chocolate (as it appears in the candy bars). The pudding base of the filling provides a place to layer in sliced bananas, which is a cream pie right there. But this pie is a good choice for the end of a light meal that might consist of a dinner salad.
For the crust:
1/2 cup pecans (2 ounces)
5 ounces vanilla wafers (40 cookies), broken into pieces
4 teaspoons dark brown sugar
1/4 teaspoon sea salt
4 tablespoons unsalted butter, melted
1/2 cup toffee or chocolate/toffee baking bits
For the filling and topping:
2/3 cup packed light brown sugar
3 Tablespoons cornstarch
1/8 teaspoon salt
3 large eggs at room temperature
1-3/4 cups milk
1 Tablespoon unsalted butter
1 teaspoon vanilla extract
2 medium bananas
1 cup chilled heavy cream
2 Tablespoons granulated sugar
Make the crust: Preheat your oven to 375 degrees. In a toaster oven or ungreased skillet, cook the pecans until lightly toasted, 3 to 5 minutes. In a food processor, combine the toasted pecans, vanilla wafers, dark brown sugar, and salt, and process to very fine crumbs. Drizzle in the melted butter and process to combine. Press the mixture into the bottom and 3/4 inch up the sides of a 9-inch springform pan, making sure the side walls are thick. Sprinkle the bottom of the tart with the toffee bits. Bake for 10 minutes to set the crust. Set aside to cool.
Meanwhile, make the filling: In a small saucepan, blend the light brown sugar, cornstarch, and salt. In a bowl, lightly beat the eggs, then whisk in the milk. Stir the milk mixture into the brown sugar mixture. Cook over medium heat, whisking constantly, until the mixture thickens, 5 to 6 minutes. Off the heat, stir in the butter and vanilla. Place a piece of buttered waxed paper or plastic wrap directly on the surface of the custard to keep a skin from forming, and set aside to cool to room temperature.
Slice the bananas on the diagonal very thinly and cover the bottom of the tart shell in two layers. Spoon the custard over the bananas and smooth the top. Cover and refrigerate until set up, at least 4 hours. Just before serving, release the sides of the spring-form.
Make the topping: Whip the cream with the granulated sugar until it is firm. Spread in an even layer over the tart, or use a pastry bag and star tip to pipe rosettes all over the top.
I have a criticism of the original recipe for this pie: the writer mentioned "stiff peaks" for the whipped cream. I thought that "stiff peaks" refers strictly to whipping egg whites into meringue. You must always take care when whipping cream, because it will turn into butter if you over-beat it. I have done this, and the process of going from whipped cream to sweetened butter is very quick. I totally didn't notice until the cream was spoiled for the purpose I intended.