2cups(200 grams) cored and chopped apples (no need to peel) I used Granny Smith apples, and I think firm tart apples work best.
1/2cup(118 ml) half and half (or heavy cream)
1cup(200 grams) packed brown sugar (use light or dark)
2cups(240 grams) confectioner's sugar, sifted
Preheat the oven to 350F Lightly spray and flour a 9x13 pan.
Whisk together the flour, sugars, baking soda, salt, and cinnamon. Set aside.
Put the butter and water in a large heavy bottom saucepan and bring to a boil. Remove the pan from the heat and whisk or stir in the flour. Then mix in the buttermilk, eggs, and vanilla, stirring just until blended, don't overmix.
Fold in the apples and turn the batter into your pan, spreading out evenly. Bake for about 30 minutes, or until the top springs back when lightly touched and a toothpick comes out without wet batter on it (moist crumbs are fine.) Let cool on a rack.
Note: wait until the cake has cooled for at least 20 minutes before making the frosting. To make the frosting, heat the half and half, butter, and brown sugar in a saucepan until it comes to a boil, stirring constantly. Take off the heat and beat in the vanilla and sifted confectioner's sugar (I like to use a whisk.) At this point I put the pan back on the warm burner and whisk or stir until any lumps disappear. The warmth will keep the frosting from setting. Quickly spread over the cake, the frosting will set up quickly at this point.
If you don't have buttermilk you can use milk, half and half, cream, or make your own buttermilk by adding a teaspoon of lemon juice to milk, half and half, or cream and let sit for 15 minutes.