On a work surface (preferably wooden), whisk together flour and salt. Mound flour mixture, then form a well in center. Add eggs and oil to the well. Cup hand around outside wall of well to prevent collapsing and, using a fork, gently break up yolks and slowly incorporate flour from the inside rim of the well. Continue until liquid is absorbed (about half of the flour will be incorporated), then knead until dough forms a mostly complete mass. If using a pasta machine to roll out dough, knead 5 minutes more to form a moderately smooth dough, adding 1 to 2 tablespoons water, if needed. (If rolling out dough by hand, knead until dough is smooth, 8 to 10 minutes more.) Wrap dough tightly in plastic wrap and let rest at room temperature 30 minutes.

To roll out dough by hand, look here for directions. To roll out by machine, divide into 4 pieces. Rewrap 3 pieces in plastic wrap. Flatten unwrapped dough so that it will fit through the rollers of a pasta machine. Set rollers of pasta machine at the widest setting, then feed dough through rollers 3 or 4 times, folding and turning dough until it is smooth and the width of the machine.

Feed pasta through machine, decreasing the setting one notch at a time (do not fold or turn pasta), to thin sheet, scant 1/16 inch thick.

Cut sheet in thirds crosswise; dust both sides of sheets with flour. Layer sheets between floured pieces of parchment or wax paper. Cover with paper and repeat with remaining dough.

With the short end of 1 pasta sheet facing you, loosely fold up sheet, folding sheet over two or three times from long ends toward the center (to fold and cut hand-rolled dough, fold 2 edges of dough round over 2 or 3 times in toward center). Turn dough 90º to cut crosswise. With a large chefs knife, cut sheet into ribbons 1/16 inch wide. Unroll strips and lightly dust with flour, then gently roll noodles into a nest, twisting once. Repeat with remaining pasta sheets.