Preheat the oven to 350 degrees F.
Lightly grease a 13 by 9-inch glass baking dish.
In a large bowl, cream together 1 stick of butter and sugar until light and fluffy. Add the eggs one at a time, beating after the addition of each.
In a separate bowl, sift together the flour, baking soda, cinnamon, and salt. Add to the wet ingredients, alternating with the sour cream and vanilla.
Pour the mixture into the prepared baking dish, spreading it out to the edges. Layer the thinly sliced apple halves on top.
To make the crumble topping, combine the sugar, flour, cinnamon, and softened butter in a bowl. Mix until it resembles coarse crumbs.
Sprinkle the crumble topping over the cake and bake until golden brown and set, for about 35 to 40 minutes.
Remove from the oven and let cool on a wire rack for at least 10 minutes.