Preheat oven to 350 and grease a donut baking pan. (You will need two 6-cup donut pans or you can do it in two batches because the recipe makes 10 donuts.)
In a large mixing bowl, combine grated carrots, pumpkin puree, egg, buttermilk, oil and vanilla. Mix well until the ingredients are completely incorporated together.
Add flour, baking powder, baking soda, sugar, salt and spices. Whisk until completely blended. Set aside to prepare streusel.
In a medium bowl, combine brown sugar, white sugar, cinnamon and flour. Mix well until all ingredients are incorporated evenly.
Pour in melted butter and carefully fold it in with a large fork. You will want to be careful so you don’t over-mix. Streusel should look like large crumbs and not paste.
Spread a little bit of streusel crumbs in the bottom of each donut cup of the baking pan.
Pour batter into a piping bag. (Depending on the bag, you might have to do it in two batches.)
Cut the tip off the piping bag, leaving only about ½ inch opening.
Squeeze batter into the donut cups of the pan, filling them. Make sure there is an even amount of batter all around.
Sprinkle donuts with streusel crumbs, generously.
Bake for 13-14 minutes. Let donuts cool in the pan for about 10 minutes and take them out onto a cooling rack.