Sata Andagi is a deep fried Japanese donut ball from Okinawa. It's colloquially called "andagi" in Hawai'i and sometimes "dango" in California. This version is a recipe from a Japanese American Obon festival, and may not be exactly the same as the traditional sata andagi you find in Okinawa but is common in Hawai'i and California.
While oil is heating, whisk flour, sugar, salt, and baking powder in a mixing bowl.
In a separate bowl, whisk eggs, milk, vanilla, and melted butter.
Mix wet and dry ingredients together. Don't overmix, but make sure no dry pockets of flour remain.
When oil is ready, scoop 1.5-2 tbsp balls of batter into the oil. The more traditional way is to squeeze the batter out of your hands from between your index finger and thumb, but you can use a cookie scoop or two spoons for convenience.
Fry dango for 5 minutes, using chopsticks to flip them halfway through to make sure they fry evenly.
Transfer dango to a wire rack to cool. Dango taste best fresh but can be kept in an airtight container at room temperature for a few days.
Notes
This style of sata andagi is the way many Japanese Americans make them for our Obon festivals. Original recipes from Okinawa use local ingredients. This recipe uses ingredients local to Americans at time of Japanese immigration in the late 19th and early 20th century.
Recipes from Hawai'i often use evaporated milk rather than whole milk, but either works.