Preheat oven to 350°F (about 177° C). Grease bottom and side of a 8 x 8-inch baking pan. Set aside.
First, make the streusel topping. Combine flour, sugar, and cinnamon in a small bowl; cut in butter with a fork until obtaining fine crumbs. Add heavy cream and vanilla, mixing well with a fork until crumbs form (the cream will add moisture to the streusel). Set aside at room temperature so that the vanilla will infuse the streusel with flavor.
In a medium bowl, combine together the sifted flour, sugar, baking powder, and salt. Pour in and then mix both the melted shortening and butter with a fork until obtaining fine crumbs.
In a separate bowl, whisk together egg, cream, and vanilla. Add to crumb mixture, tossing gently with a fork or by hand until mixture forms a ball. Press dough in an even layer into the prepared baking pan. Arrange apple slices on top of crust and then sprinkle the reserved streusel evenly over apple slices.
Bake for about 35-40 minutes or until a toothpick inserted in the center comes out clean. Let cool on a rack and slice into squares. Serve apple crumb cake plain (the traditional manner) or warm and drizzled with either caramel sauce or dulce de leche sauce and accompanied by a scoop of ice cream.