In a dry pan, toast the oregano for 1 to 2 minutes, until golden but not burned.
In a small bowl, whisk the lime juice, salt, pepper and oregano together. Drizzle in the olive oil, whisking constantly until emulsified.
Trim the stalks of the fennel down to the bulb and discard. Quarter the bulbs and trim away the triangle of core at the base. Slice the fennel as thinly as possible.
In a serving bowl, toss the fennel, red pepper and the dressing together until the vegetables are evenly coated. Serve immediately or refrigerate, covered, for up to 1 hour before serving, and toss again just before serving.
c.1997, M.S. Milliken & S. Feniger, all rights reserved