Place the walnuts in a small pan set over medium heat. Cook, stirring occasionally, until fragrant and lightly browned, five to seven minutes. Transfer to a small bowl to cool completely, then roughly chop.

Preheat a gas or charcoal grill, or set a grill pan over medium heat. While it heats, whisk together the vinegar, brown sugar, and mustard in a medium bowl. Season with salt and pepper. Slowly drizzle in the olive oil, whisking continuously until the dressing is combined and thickened.

Brush the grill or grill pan with oil. Grill the pears, turning once with tongs, until grill marks form and the pears are tender but not falling apart, two to three minutes per side.

Combine the fennel and arugula in a large shallow bowl. Drizzle with about two-thirds of the dressing and gently toss to coat. Arrange the pears on top and sprinkle with the walnuts. If desired, drizzle with the remaining dressing and sprinkle with pepper. Divide the salad among plates and serve immediately.