• Preheat oven to 220°C (425°F). Line a jumbo 6-cavity muffin pan with muffin liners (store-bought or homemade tulip liners will work), or generously grease it with melted vegan butter.
• Divide the apples into two unequal portions, one slightly larger than the other. The larger portion (around 300g or 2 1/2 cups) is for the muffin batter and the smaller portion (around 260g or 2 heaped cups) is for the topping.

Make the apple topping:

• Add the smaller portion of apples and the topping ingredients (brown sugar, butter, flour and cinnamon) to a large saucepan and stir until combined.
• Place the saucepan over high heat and cook until the butter has just melted. Reduce to medium-low heat and simmer for around 10 minutes or until the apples are tender with a slight bite and the sauce has thickened. If the sauce evaporates too quickly and the apples haven't softened, add a splash of water, lower the heat and continue cooking. Set aside to cool completely.

Make the crumble topping:

• Add all the ingredients (flour, sugars, melted butter and cinnamon) to a small bowl and mix until combined. Set aside in the freezer to firm up.

Make the muffin batter:

• Add all the dry ingredients (flour, sugars, raising agents, cinnamon and salt) to a large mixing bowl and mix until combined. Add the remaining wet ingredients (milk, applesauce, oil, vanilla, vinegar) and mix until just combined. Initially, the batter will feel very thick but it'll loosen after a few minutes. Add the reserved raw apples and gently fold through.

Assembling and baking the muffins:

• Divide batter between the muffin cups, filling each nearly to the top.
• Spoon the gooey apple topping over each muffin. Sprinkle the crumble on top.
• Bake the muffins at 220°C (425°F) for 5 minutes. Keeping the muffins in the oven, reduce the temperature to 180°C (350°F) and bake for another 28-32 minutes. The muffins are ready when the tops are lightly golden brown and the crumble doesn't look wet. If you insert a toothpick in one of the middle muffins, it shouldn't have any wet batter on it (gooey apple bits or moist crumbs are fine). Try to insert the toothpick in a few spots to check for doneness. If you make the muffins without the apple or crumble topping, bake them for 5-10 minutes less.
• Cool the muffins in the pan for 10 minutes, then transfer to a wire rack.
• Enjoy the muffins warm or at room temperature. Store them in an airtight container at room temperature for 2 days, in the fridge for 3 days or in the freezer up to 1 month. The crumble topping will soften after 1 day.