Preheat the broiler. Place the tomatillos, cut side down, on a small rimmed baking sheet. Broil for about 5 minutes, until charred all over. Remove from the oven and let cool slightly.
Place the tomatillos, lime juice, garlic, jalapeño, and salt in the bowl of a food processor and pulse until smooth. Transfer to a small bowl and stir in the onion and cilantro. Chill in the refrigerator until ready to use.
Preheat the oven to 375°F. Heat the vegetable oil in a large skillet over medium-high heat. Season the halibut fillets on both sides with salt and pepper. Add the fillets to the pan and sear for 2 to 3 minutes per side, until golden brown. Transfer the pan to the oven and cook for another 4 to 6 minutes, until the fish is cooked through and flakes easily.
Meanwhile, bring a medium pot of salted water to a boil. Add the snap peas and cook for 2 minutes. Transfer the snap peas to a bowl of ice water to stop the cooking process. Whisk together the lemon juice, olive oil, and chives in a small bowl and season with salt and pepper, to taste. Drain the sugar snap peas and toss with the vinaigrette.
To serve, place a large spoonful of salsa verde on each of four plates. Top each plate with a halibut fillet and some snap peas.