Start by browning ½ cup of salted butter. You'll melt 1 stick of butter in a medium saucepan, and then continue to cook past the point of boiling. You will do this over medium heat, past the point of the butter foaming, until it turns a nice golden brown, and has a nutty smell. Make sure you are stirring and watching it, because it will turn from perfectly brown to burnt fairly quickly. Once finished browning, pour all of it into a bowl and allow to cool completely. If you want to rush the process you can stick it in a fridge or freezer for 10-15 minutes.
Preheat oven to 350 F. Line muffin tins with liners, or spray with non-stick spray and set aside. I like to use two muffin pans and space out my liners for a higher rise on my muffins.
In a small bowl mix together the flour, brown sugar, cinnamon and salt for the crumb topping. Add in the melted butter and mix again until you have large and small bits. Set aside.
In a medium bowl, whisk together browned butter, oil and sugar until completely dissolved. Stir in eggs, vanilla, buttermilk and sour cream.
Whisk in the baking powder, baking soda, salt and flour.
In another small bowl mix together the brown sugar and cinnamon for the swirl.
Scoop about 2 tablespoons of muffin batter into your muffin cups. Followed by 1 tablespoons of the brown sugar & cinnamon on top of that.
Top with another 2 tablespoons of muffin batter and a good amount of the crumb topping.
Bake for 20-23 minutes, or until a toothpick inserted in the middle comes out clean. Allow to cool in muffin tin.
Sprinkle with powdered sugar.