In a medium bowl, combine lemon juice, olive oil, salt, and pepper.
Remove the greens from the fennel bulb, and quarter it. Add the bulb quarters to the bowl and toss to coat.
Grill fennel over medium-high heat until it just begins to soften (about 9 minutes) turning occasionally. Reserve the lemon juice and oil In the bowl.
Slice the grilled fennel into strips and add, along with the honey, to the lemon juice and oil. Toss thoroughly.
Thinly slice the red onion and add to the fennel.
Roughly chop the parsley and fennel greens. Add to the bowl with fennel bulb and onion. Toss thoroughly. Allow the slaw to cool fully.
Serve over greens as a salad, or on its own as a side for burgers or sandwiches.