Cookies and Cream Chocolate Doughnuts

INGREDIENTS

For the doughnuts::

2/3 cup

or 65 grams) cocoa powder, preferably Dutch-process

1 3/4 cups

or 223 grams) all-purpose flour

1 cup

packed light brown sugar

1 tsp

baking powder

1 tsp

baking soda

3/4 tsp

salt

large eggs

3/4 cup

milk

2 tsp

vanilla extract

2 tsp

white vinegar

1 stick

butter, melted

For the icing::

2 cups

or 250 grams) powdered sugar, sifted

4 tbsp

milk

1 tsp

vanilla extract

Oreo cookies, crushed