Preheat your oven to 350°F (175°C) and line a muffin tin with paper liners or lightly grease it.
In a large mixing bowl, whisk together the sifted flour, sugar, baking soda, cinnamon, nutmeg, and salt until evenly combined.
In another bowl, stir together the pumpkin puree, apple cider, vegetable oil, and eggs until smooth and well combined, filling the kitchen with a warm, spiced aroma.
Pour the wet ingredients into the dry and gently fold everything together with a spatula until just combined; avoid overmixing to keep the muffins tender.
Use an ice cream scoop or a large spoon to evenly distribute the batter into the prepared muffin tin, filling each cup about two-thirds full.
Mix the flour, brown sugar, oats, and a pinch of salt in a small bowl for the crumble topping. Cut in the cold butter with a pastry cutter or your fingertips until the mixture resembles coarse crumbs.
Sprinkle the crumble generously over each muffin, pressing down slightly to help it adhere and create a crispy crust during baking.
Bake the muffins in the preheated oven for about 20 minutes, or until a toothpick inserted into the center comes out clean and the tops are golden brown.
Remove the muffins from the oven and let them cool in the pan for 5 minutes, allowing the crumble to set slightly.
Transfer the muffins to a wire rack to cool completely; watch as the tops develop a lovely crisp, and the pumpkin aroma fills your kitchen.
Enjoy these moist, flavorful pumpkin muffins with their crunchy crumble topping as a perfect autumn treat.