Heat a gas grill to medium high. Put the arugula in a large bowl, cover with a damp paper towel, and refrigerate. In a blender, combine the lemon juice and zest, anchovies, garlic, and peppercorns with 6 Tbs. of the oil, 1 Tbs. of the mustard, and 1/2 tsp. salt. Blend thoroughly until most of the peppercorns are well broken up and the dressing is emulsified. Add 2 Tbs. of the grated Parmigiano and blend to incorporate. Leave the dressing in the blender.
In a medium bowl, toss the chicken with the remaining 1 Tbs. mustard and 3/4 tsp. salt. Brush the bread with the remaining 2 Tbs. oil and season with salt. Grill the chicken, covered, until golden grill marks form, 5 to 6 min. (for even cooking, rotate the chicken 90 degrees halfway through cooking each side). Flip the breasts and continue to cook, covered, until golden grill marks form and the chicken is cooked through, 5 to 6 min. Let rest on a cutting board for 5 min. Grill the bread until dark around the edges and golden brown in the center, 1 to 2 min. per side. Slice the chicken thinly on an angle. Cut each bread slice into 10 cubes. Pulse the dressing in the blender; add a little of it to the arugula, just to coat.
Divide the arugula among four plates and sprinkle with a little Parmigiano. Toss the chicken with the remaining dressing and arrange over the arugula. Sprinkle with the remaining Parmigiano and arrange the croutons and tomatoes (if using) around the salad.