Whisk together gluten-free flour blend, chickpea flour, and salt in a large bowl. Whisk eggs and oil in a small bowl to combine.
Add egg mixture to dry ingredients and stir with a fork to incorporate; mixture will be crumbly. Tip out onto a surface and knead until a smooth dough forms, about 3 minutes. Form dough into a ball and wrap tightly in plastic. Chill at least 1 hour and up to 1 day to allow flour to hydrate (the longer you can let it rest, the better).
Roll out pasta according to pasta machine directions or roll out and cut by hand.
