Place flour in work bowl of food processor fitted with steel blade. Add eggs and process until dough comes together and forms ball that rides around on top of blade. If mixture is too dry and fails to form ball, slowly add just enough water to bring ball together, no more than 1 tablespoon.
Dough ball should be slightly sticky. If too sticky and soft, add flour 1 teaspoon at time until texture is correct.
Knead dough by running processor. Ball with ride around on top of blade, becoming more and more smooth. When smooht enough, remove from processor. Wrap in plastic wrap. Let stand at least 45 minutes.
Roll dough out in pasta machine. Divide in quarters and work with 1 portion at time, keeping remainder wrapped in plastic wrap. Flatten dough, then run through machine on widest setting. Fold double and run through again, folded edge first. Repeat 2 or 3 times. Fold double again, and run through sideways. Repeat 2 or 3 more times. Dough will change from fairly sticky and possibly slightly dimpled on 1 side to satiny and smooth. Sheet should be as wide as baking dish (if not, layer dish with 2 sheets rather than 1).
Change pasta machine to next-narrower setting. Run dough through machine once. Repeat until next-to-last setting. Before rolling out at next-to-last setting, cut pasta sheet in half. After rolling out at next-to-last setting, lay pasta sheet on lightly floured dish towel and cover with another dish towel.
Repeat until all dough has been rolled out.
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