Heat a gas grill to medium high or a charcoal grill to medium hot. In a small bowl, stir together 1 Tbs. of the olive oil, the mustard, 1 tsp. salt, and about 5 grinds of pepper. Slather both sides of the chicken thighs with the mustard mixture. Toss the scallions and the mushrooms with the remaining olive oil, coating them well. Sprinkle with 1 tsp. salt and several grinds of pepper.
When the fire is hot, set the chicken, scallions, and mushrooms on the grate. Grill, turning once or twice, until the chicken is cooked through, about 8 minutes, and the vegetables are tender, about 4 minutes for the scallions and 8 to 10 minutes for the mushrooms. Transfer to a clean cutting board and loosely cover with foil.
At this point, you can proceed with assembling the salad while the chicken and vegetables are still warm, or you can set them aside and combine them at room temperature. Toss the salad greens in a large, shallow bowl. Cut the chicken and mushrooms into 1/2-inch slices; arrange on top of the the greens. Scatter the scallions, cheese, tomatoes, roasted red pepper, olives, and croutons (if using) over the salad. Just before serving, sprinkle the salad with salt and a few generous grinds of pepper. Toss the salad with enough of the vinaigrette to lightly coat the ingredients (about 1/2 cup). Serve immediately, passing the rest of the dressing at the table.
I like to add thinly sliced grilled asparagus to this salad, too. Try tossing this salad with just a little balsamic vinaigrette. After serving the salad, drizzle each portion with creamy black pepper dressing.