Preheat oven to 375 degrees F (190 degrees C). Grease 2 baking sheets.
Beat sugar and butter with an electric mixer in a large bowl until smooth and creamy. Beat eggs, 1 at a time, into creamed butter until smooth; add vanilla extract and beat well.
Sift flour and baking powder together in a bowl. Gradually stir flour mixture into butter mixture, mixing well after each addition, until dough is smooth.
Generously flour your hands. Make walnut-size balls from the dough and press into 4-inch circles on a floured surface, making the circles thicker in the center and thinner on the edges. Spoon about 1 1/2 teaspoons koshi an in the center of each dough circle. Gather the edges together and pinch dough around the filling until sealed. Place dough balls, pinched-side down, on the prepared baking sheets about 2 inches apart. Brush dough balls with evaporated milk.
Bake in the preheated oven until tops are lightly browned, about 15 minutes.