In large bowl, whisk together brown rice flour, tapioca starch, and xanthan gum. Add eggs. Switch to a wooden spoon and stir until a dough forms. Generously dust your counter with brown rice flour. Turn dough out onto counter and knead a few times until fairly smooth.

Divide dough into four equal pieces and work with 1 piece at a time, keeping the rest covered. Press the dough to flatten it slightly. Using a pasta machine set at the widest setting, run the dough through 2 times. Continue rolling dough through successively narrower settings until you reach the second-to-last setting.

Cut dough sheet in half horizontally and pass each through the fettuccine cutter. (The spaghetti setting is too thin for this gluten-free pasta.) Dust pasta with brown rice flour and place on a rimmed baking sheet. Repeat with remaining dough pieces.

Bring a pot of salted water to a boil. Cook half the batch of pasta until tender, about 5 minutes. Toss with sauce. Repeat with remaining pasta. Serve immediately.