Preheat oven to 400°F/200°C. Line muffin tins with papers or spray muffin compartments with vegetable spray.
In a bowl stir together the sugar, cinnamon, and flour. Drizzle with vegan butter and stir to combine until you achieve a crumbly mixture. Don't overmix. Set aside.
In a medium bowl stir together the oil, sugars, applesauce, milk, and vinegar. Stir to combine.
In a large bowl stir together the flour, cornstarch, baking powder, baking soda, cinnamon, and salt. Create a well in the middle of the flour. Pour the milk mixture in and stir until just combined.
Pour the batter into prepared muffin tins. Use a spatula to get every last bit of the batter. Spoon the crumble topping evenly across the muffins. Use your hand to gently tamp down the crumble topping. Bake for 5 minutes, then leaving muffins in the oven, turn the oven temperature down to 350°F/175°C. Bake for another 16 - 17 minutes until a toothpick inserted in the middle comes out clean. The crumble topping should be nice and golden brown as well.
When done, remove from the oven and allow to cool for 10 minutes before drizzling with icing.
For the Icing Drizzle
Prepare the icing by adding powdered sugar to a bowl. Add milk and whisk.
Store muffins in an airtight container at room temperature for up to 3 days. These muffins can be refrigerated up to 7 days or frozen for up to 1 month.
Regarding flour, this recipe uses all-purpose flour. You can substitute 1:1 Whole Wheat Pastry Flour, but note, this is not the same as whole wheat flour. If you don't have whole wheat pastry flour, either use 100% all-purpose flour, or 1 cup all purpose flour combined 1/2 cup whole wheat flour.Make Ahead Instructions: For longer storage, freeze muffins (with or without icing) for up to 3 months. Allow to thaw overnight in the refrigerator, then bring to room temperature or warm up in the microwave if desired. Top with icing before serving if needed.