Preheat the oven to 350°F (177°C). Spray an 8-inch (20cm) square baking pan with cooking spray. Set aside.
In a small bowl, combine the crumble ingredients together. Set aside.
In a large mixing bowl, whisk together the flour, sugar, baking soda, salt and pumpkin pie spice.
In another bowl, whisk together the apple cider, oil, extract and vinegar.
Add the wet ingredients into the dry ingredients and stir with a rubber spatula until blended.
Scrape the batter into the prepared pan. Sprinkle the apples over the top.
Break up the crumble mixture into pieces with your fingers and sprinkle on top of the cake.
Bake until golden brown and a toothpick inserted into the center of the cake comes out clean, about 30 minutes.
Cut into squares and serve.
