Step 1

Position a rack in the middle of the oven and preheat to 425 degrees.

Step 2

In a small bowl of food processor or mini-processor, combine the parsley, shallot, mustard, lemon juice and 1/8 teaspoon each of the salt and pepper, and pulse until finely chopped. Drizzle in 3 tablespoons of the oil and continue to process, stopping to scrape down the sides if needed, until the mixture is smooth and creamy. (If your processor allows for the oil to be drizzled with the motor running, do that.) You should see tiny flecks of parsley in the emulsified sauce. Transfer the sauce to a jar.

Step 3

On a large, rimmed baking sheet, arrange the broccolini in a single layer and drizzle with the remaining 1 tablespoon of oil. Season with 1/8 teaspoon of salt, toss to coat, then push the broccolini to one side of the baking sheet. Arrange the fish onto the other side and season with the remaining 1/8 teaspoon each of salt and pepper.

Step 4

Roast for 12 to 15 minutes, or until the fish flakes easily with a fork and the broccolini stems are tender and the tops are lightly crisped.

Step 5

Divide the fish and broccolini among 4 plates. Top the fish with the parsley sauce and serve.