Preheat oven to 400°F (200°C).
Trim the broccolini ends and rinse thoroughly. Toss in a small bowl with a pinch of salt and 1 tablespoon olive oil.
Season chicken breast with salt and pepper on both sides.
Heat an oven-safe skillet over medium-high heat and add the remaining olive oil.
Once hot, add the chicken. Sear 2–3 minutes on the first side.
Flip and brush all sides with Dijon mustard. Continue searing another 2 minutes.
Add broccolini to the skillet, tossing to coat in the juices.
Transfer skillet to oven and roast 8–12 minutes, or until internal chicken temp reaches 165°F.
Remove skillet and let rest 2–3 minutes. Slice chicken into ¼–½ inch pieces.
Plate with roasted broccolini and finish with a generous spoonful of rouille.