Combine the dry ingredients in a large mixing bowl. Pour over the boiling water, then set aside for 20 minutes for the dough to cool.
Once sufficiently cooled, mix in the eggs. Stir the dough as much as you can, then tip it out onto a clean dry bench. There will likely be lots of dry bits and errant flour. Continue to knead the dough until it comes together in a smooth ball with no dry flour bits.
The dough should be smooth with no dry bits but stiff. It shouldn’t feel crumbly or like it could easily crumble in your hands, but it also shouldn’t feel wet.
If it isn’t the right texture, make amendments (add a small amount of water or flour until you reach the described consistency).
Liberally flour your bench with tapioca flour and divide the dough in 4 or 5 equal sized balls. Cover all but one.
Use a rolling pin to roll the dough out into a long rectangle, thin enough to thread through the pasta machine. Trim the scraggly edges to ensure the rectangles are easy to put through your pasta machine. The pasta expands during cooking, so roll the dough thinner than you'd like your pasta.
You can restore scraggly bits by kneading in small splashes of water until you reach the desired consistency.
Cut your sheets by carefully feeding them through the fettuccine style cutter for thicker pasta noodles. Assemble each group of cut pasta in small nests on the bench or a clean, dry board. You can gather up and scrappy bits and roll them into the next ball of dough. Continue until all the noodles have been cut.