In a medium mixing bowl, whisk together flour, sugar, baking powder, and salt. Set aside.
In a separate bowl, whisk together eggs, evaporated milk, and vanilla extract. Gradually fold the wet mixture into the dry ingredients until a thick, sticky dough forms. The batter should resemble cookie dough—thick, not pourable. You may not use all the wet ingredients. Do not overmix.
In a medium pot or Dutch oven, add oil for frying and heat to 325–350°F. Use a thermometer for accuracy. Oil depth should be at least 2–3 inches so andagi can easily float and roll.
Using a small scoop, form rough 1-inch balls. Do not pack tightly, imperfections create the classic cracked texture.
Carefully lower 3-5 dough balls into the hot oil at a time. Fry for 4-6 minutes, turning as needed, until evenly golden brown. If outside cooks too quickly, lower oil temperature slightly.
Check doneness by inserting a toothpick in the center of the andagi. If toothpick comes out clean, your andagi is done.
Remove with a slotted spoon and drain on paper towels or wire rack. Serve warm or cooled.