Heat about 2 inches of vegetable oil in a deep pot over medium heat until it reaches 350°F.

In a large mixing bowl, combine mochiko sweet rice flour, gluten-free 1:1 flour, granulated sugar, baking powder, and salt, whisking until blended.

In a separate bowl, whisk together large eggs, warm milk, and melted unsalted butter until smooth.

Pour the wet ingredients into the dry ingredients, mixing gently until the batter is smooth.

Drop dollops of the batter into the hot oil, frying for 3–5 minutes on each side until golden brown.

Remove donuts from the oil and place on paper towels to cool for about 10 minutes.

Whisk together powdered sugar, milk, and vanilla bean paste until smooth to prepare the glaze.

Dip the tops of the cooled donuts into the glaze or drizzle it over them, then set on a wire rack to allow the glaze to set.

Serve immediately for the best texture, or enjoy throughout the day.