In a medium saucepan, heat the milk, heavy cream, vanilla bean or extract, and half the sugar to a simmer (just below a boil). In a small bowl whisk together the egg yolks and the rest of the sugar and temper it by adding a small amount of the heated milk mixture to the bowl while whisking constantly (known as a liaison). Now pour the liaison (egg mixture) into the milk pot, stirring constantly. You are only heating it. Do not boil. Do not cook. The idea is to avoid making scrambled eggs! Continue cooking on medium heat until the mixture begins to thicken so it will coat the back of a spoon, about 5 minutes. Remove from heat and allow to cool.
In a large skillet, saute the apples and bananas in the butter and add cinnamon and lime juice and stir to coat. Bring to a simmer over medium heat and allow to cook until apples are tender and caramel colored, about 20 to 25 minutes and let cool.
For the crumb topping, using a wooden spoon, mix oatmeal, flour, sugar and butter until the mixture resembles bread crumbs.
Combine the now cooled apples with the cream, pour into the pie shell and top with oatmeal mixture. Bake until crust is completely baked and golden brown, about 15 minutes.
Heat maple syrup as an accompaniment, and serve.