In another bowl, prepare the topping: Mix together the brown sugar, flour, oats, baking powder, and salt. Cut in the dairy-free butter with a pastry cutter, or just mix in chunks of dairy-free butter by hand until there are only pea-sized or smaller pieces left in the topping.
Toss the bowl of apple filling mixture again with a spoon, then pour into the prepared 8x8 dish. Spread the prepared topping over the apples.
Nutrition analysis (approximate per serving): 336 calories, 10.5 g fat, 4.5 g saturated fat, 225 mg sodium, 61 g carbohydrate, 3 g fiber, 43.5 g sugar, 2.5 g protein, Vitamin D: 0%, Calcium: 4%, Iron: 6%, Potassium: 4%