Combine butter and sugars in a large bowl and use an electric mixer to beat until creamed together.
Add egg yolks and beat until ingredients are well combined.
Add vanilla extract and sour cream and stir well (be sure to scrape the sides and bottom of the bowl if using a stand mixer).
In a separate bowl, whisk together flour, baking powder, cornstarch, salt, and nutmeg (if using).
Add dry ingredients to wet and use a spatula and stir by hand until ingredients are combined (I don't recommend using your electric mixer at this point, you don't want to over-work the ingredients or it can make your donuts tough).
Cover your bowl with plastic wrap and refrigerate for at least one hour.
Once dough has chilled, remove from refrigerator and turn out onto a clean, lightly floured surface. Use a rolling pin to roll to about ½" thickness and use a donut cutter to cut out donuts (save the holes, I always fry the donut holes as well!).
Re-group any scraps and work them together, re-roll out, and repeat to cut out as many donuts as possible from your dough.
Transfer cut out donut shapes to a wax paper lined cookie sheet and return to the refrigerator for at least 15 minutes while you heat your oil.
While dough is chilling, fill a Dutch oven at least 2-3" deep with canola or vegetable oil. Fix a candy thermometer to the edge (make sure it is in the oil but not touching the bottom of the pan) and set your heat to medium-low. Oil will need to reach 350-360F (175-185C) before you can continue. Meanwhile, prepare your glaze.
To prepare the glaze, combine melted butter, sugar, vanilla, and hot water in a small bowl and whisk or stir until smooth. Set aside.
Once oil has reached 350-360F (175-185C), remove donuts from the refrigerator and use tongs to carefully transfer donuts or donut holes in the oil, just 3 or 4 at a time. Adding donuts will cause your oil temperature to drop, so make sure you allow it to come back to the correct temperature between batches.
Allow to cook for about 1-1 ½ minutes and then use tongs to flip. Cook another 1-1 ½ minutes and then use tongs to remove them from the oil and transfer to a paper towel lined plate. Allow to cool 1-5 minutes.
Dip donuts in prepared glaze and then transfer to a cooling rack to allow the glaze to set.
Enjoy warm. Donuts will keep for several days in an airtight container at room temperature, but they really taste best warm and freshly fried.
*This seems to be the average number of donuts I get while doing the least amount of re-rolling of the scraps. I try to keep the re-grouping/re-rolling to a minimum to not over-work the donut dough, as this can make your donuts tough.**Don't feel like making a glaze? You can dip these donuts in granulated sugar or a mixture of ⅓ cup granulated sugar and 2 teaspoons of cinnamon. Dip the donuts in the sugar right after removing them from the oil.