Combine dry ingredients in a large bowl: glutinous rice flour, black sesame powder, sugar, baking powder, salt. Combine wet ingredients in a measuring cup: warm milk, oil, egg. (I add the milk first then heat in the microwave for 30 seconds. After removing from the microwave,I add the oil and egg.) Add wet ingredients to dry ingredients and mix with a fork until large clumps form.
Gather clumps with hands and form into a large ball. Knead until smooth, about 1-2 minutes. It will be very sticky. (Feel free to add more rice flour, up to 1/2 cup, if it's too sticky to handle).
Generously flour a work surface with rice flour. Transfer dough and roll out until 1/2-inch thick. Cut into 3-inch circles and donut holes. Knead the scrap pieces and keep cutting until you have 8-10 donuts. (Again, the dough will be very sticky so be sure to generously flour with rice flour - the rolling pins, the biscuit cutters, the dough.)
Prepare for deep frying: Fill a cast iron dutch oven with 1-2 inches of neutral oil with a high smoke point. (I use grapeseed oil.) Clip a candy thermometer and line a baking sheet with paper towels.
Heat oil on medium heat until the temperature reaches 350F/175C. Add donuts, making sure not to overcrowd the pan. Fry until golden and puffy, about 1-2 minutes on each side. Transfer to paper towel lined baking sheet to drain oil. Keep frying in batches until all donuts are fried on both sides. Keep an eye on the thermometer and adjust heat level so the temperature stays between 340-350F. (Make sure not to overcook! When you take a bite, the donut should be chewy and a little bit stretchy. It's ok if it doesn't look fully cooked, that's the nature of mochi. As long as it's not raw, it's better to undercook rather than to overcook.)