How to Make It
Preheat broiler with rack about 6 inches from heat. Stir butter, tarragon, and chives in a small bowl; set aside.
Place potatoes in a large saucepan and cover with cold water. Bring to a boil over high and cook until just tender, 12 to 13 minutes. Add Broccolini and cook until crisp-tender, about 4 minutes. Drain; transfer potatoes to a cutting board and set Broccolini aside. Smash potatoes, 1 at a time, with the bottom of a bowl until flattened slightly.
Drizzle 2 tablespoons oil over both sides of fish fillets; season with ½ teaspoon salt. Coat a baking sheet with cooking spray. Place fish, skin side up, on baking sheet and broil until skin is crispy and fish flakes with a fork, about 10 minutes.
Meanwhile, heat 1 tablespoon oil in a large skillet over medium-high. Add potatoes and cook, undisturbed, until golden, about 2 minutes. Add remaining 1 tablespoon oil, flip potatoes, and cook, undisturbed, until golden, about 2 minutes. Add Broccolini; cover and cook until warmed, about 1 minute. Add 2 tablespoons herb butter and remaining ½ teaspoon salt; toss to coat. Serve with fish and remaining herb butter.