Preheat oven to 450 degrees. Rub outside of pepper with olive oil, and place on a small baking sheet. Cook until skin begins to bubble and lightly brown in spots, 20 to 25 minutes, turning once after 10 minutes. Transfer to a container with a tight-fitting lid to steam, about 15 minutes. Remove stem and seeds; peel away skin, and discard.
In the bowl of a food processor fitted with a steel blade, puree pepper (there should be a generous 1/2 cup puree). Add flour and eggs. Process until dough forms a ball, about 20 seconds. Transfer dough to a lightly floured work surface. Knead until smooth and elastic, about 5 minutes. Cover with an inverted bowl or plastic wrap, and let rest 1 1/2 hours at room temperature, or refrigerate overnight.
Divide dough into 8 pieces. Working with a few pieces at a time and keeping remaining pieces covered, flatten each portion of dough into a disc shape somewhat narrower than the pasta machine opening. Very lightly dust dough with flour. Feed through at machine's widest setting. (If dough pulls or tears when passing through the machine, simply sprinkle a little more flour over the dough just before it's fed to keep it from sticking; when finished, remove excess flour with a dry brush.) As pasta sheet emerges, gently support it with palm, and guide it onto work surface. Fold sheet in half. Pass through a second time on the same setting to smooth dough and increase its elasticity.
Thin dough by passing it through ever-finer settings, two passes on each setting, until sheets are almost translucent but do not tear. (On the Kitchen Aid attachment, the dough was passed through settings one through four, but keep in mind that machine settings differ; some have as many as 10, while others have only six).
Switch to the cutter attachment, and pass each sheet through fettuccini cutter. Separate strands, and hang on a pasta rack to dry so they do not stick together.