Preheat the oven to 425F.
Start by making the cherry filling. Combine all the ingredients for the filling in a large saucepan over medium heat. Bring to a boil. Reduce heat to a simmer and simmer for 5 minutes, stirring occasionally, until the cherries are tender and the juices have thickened. Transfer cherries to a 9x9 baking dish.
To make the crumble topping combine flour, sugar, baking powder, baking soda, and salt. Add the butter in small cubes and mix it in with the dough using your fingers until small pea-sized pieces have formed. Add non-dairy milk and stir together until a stiff dough has formed. You may need to add a little more milk. If so, add it 1-2 teaspoons at a time.
Drop pieces of dough onto the cherry filling so that it is mostly covered with a large piece of dough.
Bake for 20 minutes, uncovered until the cherries are bubbling up and the dough is golden brown. Remove from the oven and let sit for 20 minutes before serving.
Serve with non-dairy ice cream of your choice.