Preheat oven to 350°F.

Spread blanched hazelnuts in a single layer on a rimmed baking sheet.

Toast hazelnuts, stirring occasionally, until golden, 8-10 minutes.

Coarsely chop the toasted hazelnuts and set aside.

Reduce oven temperature to 300°F.

Scatter fresh tarragon sprigs on a large rimmed baking sheet.

Place halibut fillet on top of the tarragon sprigs.

Drizzle halibut with 2 tablespoons olive oil.

Season halibut with kosher salt and freshly ground pepper.

Roast halibut until it is just opaque in the center, approximately 20-30 minutes, depending on the thickness of the fish.

Meanwhile, melt unsalted butter in a small saucepan over medium-high heat.

Cook butter, stirring often, until it foams and then browns (do not let it burn), about 5 minutes.

Remove browned butter from heat.

Let brown butter cool slightly.

Stir in fresh lemon juice, chopped hazelnuts, and remaining 2 tablespoons olive oil into the brown butter.

Season the hazelnut brown butter sauce with salt and pepper.

Serve the roasted halibut with hazelnut brown butter sauce and lemon halves.