HIT THE HEAT
Preheat the oven to 350 degrees . In a large, ovenproof skillet fitted with a lid, melt the butter over medium heat. Pat the halibut dry; season with salt and pepper. Place flesh side down in the pan and sear for 2 minutes. Using a spatula, carefully flip to sear the other side, 2 minutes more. Transfer to a plate. In the skillet, heat the EVOO over medium-high heat. Add the leek and garlic; cook, stirring, for 2 minutes. Add the clams and cook, shaking the pan, 1 minute.
Add the wine, 3/4 cup water, the carrots and potatoes; cover. Cook, transferring the clams to a plate as they open, for 5 minutes.
COVER AND SIMMER
Return the halibut to the skillet; cover and transfer to the oven. Braise until the fish is cooked through and the veggies are tender, 16 to 18 minutes (as shown above).
FINISH THE DISH
Transfer the halibut to a cutting board; halve each piece crosswise and divide, along with the veggies, among 4 shallow bowls. Add the clams and tarragon to the skillet. Cover and bake for 1 minute. Add to the bowls.