Preheat the oven to 350F. Oil or lightly grease a 9-inch pie dish (not necessary if you use a nonstick pie dish).
Chop the cranberries (pulsing them in a food processor makes this easy). Transfer the chopped cranberries, walnuts, and cane sugar to the pie dish.
In a mixing bowl, whisk together the flour, baking powder, salt, and cane sugar. In a separate bowl, combine the milk and vinegar and allow them to sit for a couple minutes. Add the vegan butter and almond extract. Stir these wet ingredients together.
Pour the wet ingredients into the dry ingredients. Mix with a spatula until you have a smooth batter (tiny lumps are OK, but no big lumps or streaks of flour).
Pour the batter over the cranberry and walnut mixture. Use an inverted spatula to spread it around the top. Transfer the pie dish to the oven and bake for 40 minutes, until the cake portion is just turning light golden at the sides. Allow the pie to cool for 10 minutes before slicing and enjoying!