Whisk the flours and sugar.
Add water. Add coconut milk and extract at this time too, if using.
Steam for 15 minutes in any sort of steamer. OR microwave in a well covered dish for two minutes and 30 seconds. I usually check for doneness and stir after two minutes.
Turn out the cooked mochi onto a cutting board or silicone mat and knead into a log. Be careful, as it will be very hot.
Cut 1/2 of the log to dye. Keep remaining 1/2 covered so it doesn't dry out.
Cut the 1/2 chunk of mochi into 4 equal pieces (or however many colors you want). Working one at a time, place one drop of food coloring on each piece and knead to evenly combine. Keep any pieces you're not kneading covered with a damp cloth. Keep hands moistened with water to keep from sticking, but do not add any more water than necessary or the dough will become too soft and sticky. If your dough starts becoming too wet, use katakuriko to keep it from sticking to your kneading surface.
Roll each colored mochi into a thin noodle about 18 inches long. Cut each noodle in half so you have two stripes of each color.
Arrange the colorful stripes to create a rainbow of alternating colors that form a rough rectangle. Please see pictures in blog post above for more detail.
Place the remaining white mochi log on top of your rainbow.
Wrap the edges of the rainbow around the white mochi, pinching to seal.
You should now have a fat mochi log with rainbow colors on the outside and white on the inside. Roll this log into a thin, long log to your desired thickness and slice into pieces. I like mine to be about marshmallow sized.
Toss the pieces in katakuriko to prevent them from sticking and store any leftovers in an airtight container at room temperature.