Trim the thin ends, and the root, from the fennel. Remove any tough or damaged parts, remove the fronds and reserve for the salad. If you prefer smaller fennel pieces in the salad, cut the fennel into quarters.
Using a mandoline (or sharp knife), thinly slice the fennel (about 1/16 inch thick).
In a large bowl, whisk together oil, lemon juice, and vinegar.
Add sliced fennel, mint (or thyme) and parsley. Toss to coat, and rest for about 30 minutes to allow the fennel to wilt and the flavors to meld.
Add salt and pepper and toss. Add reserved fennel fronds to the salad and serve (or garnish served portions with the fronds).
Choose thyme over mint if making this salad ahead of time, or plan on having leftovers, because thyme tends to last longer than mint does.
Refrigerate fennel salad in a covered container for up to 3 days.