In a medium bowl whisk to combine yolks and cornstarch. In a blender combine milk, sugar, and bananas and blend until smooth. Strain into a medium saucepan.
Bring milk mixture to a simmer over medium heat, then whisk half of it into the yolk mixture. Whisk the yolk mixture into the remaining milk mixture in the saucepan and place over medium heat. Bring to a simmer and cook, stirring constantly, for 1 minute, then scrape into a bowl.
Place a piece of plastic wrap directly on the surface of the custard and refrigerate until chilled, 3-4 hours.
In a large bowl or a stand mixer fitted with the dough hook combine 2 cups flour, sugar, yeast, and salt. Add milk and yolks and stir to combine until a dough forms. If dough is very wet and sticky add up to ¼ cup more flour 1 tablespoon at a time. Knead or mix in butter and continue to knead or mix until dough is smooth and soft, about 5 minutes.
Transfer dough to an oiled bowl and turn to coat with oil. Cover tightly and let rise in a warm place until nearly doubled, about 1½ hours.
Transfer dough to a lightly floured countertop and knead briefly to deflate it. Roll out dough to ¼” thick. Use a 2¼” round cutter to cut out as many rounds of dough as possible. Gather the scraps and knead briefly to bring them together, then roll out again and cut more rounds.
Lightly oil a large baking sheet and place dough rounds on it, leaving ½” space between them. Cover loosely with oiled plastic wrap and let rise until puffy, about 30 minutes.
Add oil to a Dutch oven or large, heavy pot until 1½” deep. Heat over medium heat to 350℉. Line a large baking sheet with paper towels and set a cooling rack on top.
Use a thin metal spatula to transfer dough rounds, in batches, to hot oil. Do not crowd pan. Fry until golden on one side, about 1½ minutes, then turn and brown second side. Use a slotted spoon to transfer doughnuts to rack to drain and cool.
Fry remaining doughnuts, taking care to keep oil temperature around 350℉.
When doughnuts are cool, poke a hole in the side of each with a paring knife. Stir custard to loosen it, and transfer to a piping bag fitted with a ¼” plain tip or a zip-top bag with a ¼” hole cut in one corner.
Fill doughnuts with custard. Dust with powdered sugar before serving.