Using a mandoline slicer, carefully shave the fennel and shallot into thin slices. Transfer to a bowl and add a pinch of salt.
Add the lettuce and arugula to the fennel and shallot and toss to coat.
Make the dressing:
Add the maple syrup, Dijon mustard, whole-grain mustard, and lemon juice to a bowl. Whisk until smooth. Slowly add the extra virgin olive oil, whisking as you incorporate until smooth and emulsified. Taste and add salt. Set aside; you may need to whisk again right before serving.
Make the Brussels sprouts:
Heat 1 tablespoon olive oil in a skillet over medium-high heat. Once shimmering, add the Brussels sprouts and use your spoon to flip as many sprouts cut-side down as possible. Season with salt. Cook without moving for 4–6 minutes to allow the sprouts to develop a nice char.
Toss the sprouts and continue cooking for 5–7 minutes until the sprouts are tender. Add more salt and pepper if needed.
Add the pecans to the skillet and cook, turning often, for 1–2 minutes until toasted. Turn off the heat.
Finish the salad:
Whisk the dressing right before serving. Add the Brussels sprouts and pecans to the salad. Pour as much of the vinaigrette on top as you like; you can serve the remaining dressing at the table or reserve it for another use. Toss to coat the salad with the dressing and add more salt if needed.
To serve:
Pile the salad onto a serving platter. If your fennel bulb had fennel fronds, scatter a few on top of the salad. Serve the salad alongside your favorite main course. Enjoy!