Season chicken breasts on both sides with salt and pepper. In a pan over medium-high heat, sauté chicken in 1 tablespoon olive oil for roughly 5 minutes on both sides.
For the salad, shave fennel bulb as thin as possible on a mandolin. Set aside in bowl of ice water. Shave red onion and toss with red onion; mix with olive oil and lemon, just enough to coat. Mix with remaining tablespoon olive oil, apple cider vinegar and whole grain mustard, and set aside.
To serve, place fennel-red onion salad in center of plate. Slice chicken breasts into five pieces each (depending on size) and lay across salad. Garnish chicken with fennel fronds. Drizzle whole grain mustard vinaigrette on and around the plate.