In a large bowl, combine melted butter, granulated sugar, vanilla extract, and vegetable oil. Whisk until well combined.
Add eggs and sour cream, whisking until just incorporated.
Add flour, baking powder, baking soda, salt, and milk. Gently mix until fully incorporated. Don't overmix!
Cover the bowl and let it sit at room temperature while preheating the oven to 425°F.
Line 16 muffin tins with liners.
Once preheated, scoop about 2 tablespoons of batter into each liner.
Top with 2 tsp of the filling, then more batter. The batter should almost reach the top of the pan.
Sprinkle the crumble on top.
Bake at 425°F for 5 minutes, then reduce the temperature to 350°F. Bake for an additional 30-35 minutes until cooked through.
Let them cool completely before adding the icing.