1. Combine oil, shallots, and a generous pinch of salt in a small bowl.
2. Quarter fennel bulb lengthwise and cut away the core. Slice quarters thinly crosswise with a mandoline or other manual vegetable slicer, or with a chef's knife.
3. Segment oranges: Working with one at a time, cut a slice off the bottom and top to expose flesh. Stand orange on a cutting board. With a small, sharp knife, slice off peel and white pith, following the curve of the fruit. Cut between membranes and fruit to release segments into a bowl. Repeat with remaining oranges.
4. Remove core and any bitter-tasting dark green outer leaves and leaf tips from frisée. Tear pale yellow center leaves into bite-size pieces to get eight small handfuls.
5. Combine frisée, fennel, and parsley in a serving bowl. Add orange segments to frisée, leaving juice behind. Add shallot oil, several grinds of pepper, and 1/2 tsp. salt and toss gently. Season with more salt and a squeeze of lemon juice if you like. Serve immediately.
Make ahead: Through step 4, up to 8 hours; cover shallot oil and leave at room temperature. Put fennel in a bowl, cover with a damp towel, and chill. Cover oranges and chill. Wrap frisée in a paper towel, put in a plastic bag, and chill.
Note: Nutritional analysis is per 1-cup serving.