Preheat the oven to 425F. Line a 12-cup muffin tin with paper liners or grease well.
For the crumb topping: Stir together ¼ cup brown sugar, ¼ cup flour, 2 tablespoons melted butter, 1 teaspoon cinnamon, ¼ teaspoon nutmeg, and ¼ teaspoon cardamom. It should be mostly crumbly.
For the muffins: In a mixing bowl, whisk together ¼ cup melted butter, oil, sour cream, and granulated sugar. The sour cream may separate, but it should come back together with more stirring. Stir in the eggs and vanilla until a cohesive golden batter forms.
In a separate bowl, whisk together 1 ½ cups of the flour, baking powder, baking soda, and salt. Stir this into the wet ingredients about 1 cup at a time, until a thick batter forms.
Sprinkle the diced apple with flour, about 1 tablespoon. Fold it into the batter.
Add a heaping spoonful (about 2 tablespoons) of batter to each muffin tin. Sprinkle with a layer of cinnamon. Top with another heaping spoonful of batter, then sprinkle with the crumble.
Bake at 425F for 5 minutes, then without opening the oven door, reduce the oven temperature to 350F. Bake for another 18-20 minutes, or until the muffins are domed (it's okay if it's just a subtle dome) and pulling away from the edges of the muffin tin.
Remove from the oven and let cool on a wire cooling rack. In a small bowl, whisk together the powdered sugar and 2 tablespoons of milk until smooth. It should be easy to drizzle. Add extra milk 1 tablespoon at a time, as needed. Drizzle the cooled muffins with the glaze and enjoy!
Notes
Storage: Keep coffee cake muffins at room temperature for up to 3-4 days.
Freezing: These muffins freeze very well. Let cool completely before freezing in an airtight container. Pop in the microwave to thaw quickly or thaw overnight on the counter.