In a bowl, combine pancake mix, mochiko, and salt. Slowly add milk to the flour mixture and mix well into a dough. Add egg, mix well until thoroughly combined.

Scrape the dough onto a surface that's dusted with more rice flour to prevent sticking. Roll the dough into a long snake, about 3/4" thick. Cut into 1" pieces and roll all the pieces into balls.

Arrange 6 or 8 balls to form a ring on a piece of parchment paper, connect them with a dab of water.

Add vegetable oil to a pot and set on medium-high. Once the oil is ready, turn the heat down to medium-low. Carefully add donut, along with parchment paper, into the oil. Remove the paper with a tong once it's detached. Fry donut for a few minutes on each side until the donuts are puffed up and golden brown. Transfer to a cooling rack.

To make the icing: melt the butter and combine with caramel sauce. Transfer to a shallow bowl. Add in 1 tablespoon of milk if icing is too thick. Dip one side of donut into the warm icing and immediately sprinkle the dipped side with salt.