In a small bowl, whisk together 1 1/4 cups flour, 2 teaspoons baking powder, and 1/4 teaspoon salt. Set aside.
In a medium mixing bowl, whisk together 1/4 cup milk, 1/4 cup buttermilk, 1/4 cup sugar and 3 tablespoons melted butter until just combined.
Use a sharp knife to split the vanilla pod open lengthwise and scrape seeds into the milk/sugar/butter mixture. Whisk until vanilla beans are thoroughly incorporated into the mixture.
Combine the small bowl of dry ingredients with the medium bowl of wet ingredients, using a rubber spatula to stir in the dry ingredients and mixing until just combined. Be careful not to overmix, or you will get dense donut holes and I will cry for you. The texture of the dough should be sticky.
Preheat 2 cups of oil over medium heat in a 10 inch pan (I used an iron skillet). Once the oil has reached 350 (F), measure out 1 tablespoon of dough using a 1-tablespoon sized cookie scoop. The cookie scoop should by default make a round shape, so there's no need to roll the dough into balls unless you want perfect looking donuts. I didn't do any rolling and mine turned out okay :-) Drop the dough into the pan of oil. Fry until golden brown on bottom then flip and cook on the reverse side until golden brown.
When the donut hole is finished frying, carefully remove with metal tongs or a fork and place on a cooling rack lined with paper towels to absorb the excess oil. When the donut hole has cooled down enough so that it doesn't burn you when you pick it up, roll in a small bowl filled with 1/2 cup sugar. Set aside.
Repeat this proces with remaining dough. You can cook more than one donut hole at a time. I was able to cook six in one go.