Preheat the oven to 375°F. Spray 15 donut cups with nonstick cooking spray. (NOTE: If you only have 1 donut pan, you can bake these in batches!).
Place sugar and scraped vanilla beans (not the pods!) in the bowl of a stand mixer. With your hands, scrape together, until the beans are evenly dispersed throughout the sugar. Add the butter, and place on the mixer fitted with a paddle attachment. Beat on medium speed until sugar and butter are well combined. Add the eggs, one at a time, mixing well after each addition, scraping down the bowl as needed.
In a separate bowl, whisk together the gluten free flour, cassava flour, baking powder, baking soda, and salt. In a measuring cup, mix together the milk and vanilla extract. Alternating the flour mixture and milk mixture, add the first ⅓ of the flour mixture to the butter mixture, and beat on medium speed. Once combined, add ½ of the milk mixture, and mix to combine. Add another ⅓ of the flour mixture, mixing just to combine, then add the rest of the milk mixture. Finally, add the remaining flour mixture, mixing until just combined.
Place the mixture into a piping bag, and pipe the mixture into the donut pans, leaving about ¼ inch at the top of the pan. Bake for 8-10 minutes, spinning the pan halfway through baking. Remove from the oven, and let cool 1-2 minutes before turning out onto a cooling rack to cool completely. If baking in batches, repeat the process with more batter, until you have used all your batter.
While the donuts are cooling, in a small bowl whisk together mascarpone cheese and powdered sugar, until thoroughly combined and smooth. Slowly whisk in the lemon juice, 1 ½ teaspoons lemon zest, coarse Kosher salt, and vanilla extract.
Once the donuts have cooled completely, you are ready to glaze! Some of the donuts may have risen so there is no hole in the center. If this is the case, and you desire a hole in the center, take the back end of a large pastry tip and press it down into the center of the donut. The back end of the pastry tip should be about 1 ½ inches in diameter. If you do not have a pastry tip, you can also use a small circular cookie cutter. The last option is to simply use a paring knife and trim out a hole.
Once a hole has been formed, simply dip the top half of the donut into the mascarpone icing. Turn the donut over and let sit for 5 minutes. For thicker icing, repeat the process. Sprinkle the donuts with the remaining lemon zest. ENJOY!