Preheat the oven to 450˚F (230˚C). Arrange the oven racks the top third and bottom third of the oven.
Bring a large pot of salted water to a boil. Add the potatoes and cook until fork-tender, about 20 minutes, then drain.
Transfer the potatoes to a rimmed baking sheet and gently smash so they flatten halfway. Drizzle a generous amount of olive oil over the potatoes, then season with salt, pepper, and 1 tablespoon of the Zesty spice blend. Spread on a baking sheet and set aside.
In a small bowl, mix together 2 tablespoons of the Zesty spice blend, 1 tablespoon salt, and 2 teaspoons pepper. Gently the pat halibut fillets dry with a paper towel. Season the fillets on all sides with spice mixture.
Arrange the halibut and green beans in a single layer on a rimmed baking sheet. Drizzle olive oil over the fish and green beans. Sprinkle salt and pepper over the beans and toss to coat. Turn the fish over to ensure all sides are coated in olive oil.
Place potatoes on the top rack of the oven and the fish and beans on the bottom rack. Roast until the potatoes are crispy, the fish is opaque in the center, and the beans are crisp but tender, 8-10 minutes.
Meanwhile, make the sauce: In a medium bowl, mix together the basil, lemon zest, and lemon juice. Drizzle in the olive oil and stir to incorporate, then season with salt and pepper.
To serve, divide the halibut, potatoes, and green beans among plates. Spoon the sauce over the fish and beans.