Bring the salt and water to a simmer and crumble in the saffron. Stir, turn off the heat and cover the pot. Let this come to room temperature, which can take a couple hours, or speed the process by putting the pot in a large pot that has ice in it. Once the saffron brine is at least at room temperature, if not cooler, submerge the halibut in it and brine in the refrigerator for at least 2 hours, and up to five hours.
Meanwhile, make the salsa verde. Put the anchovies, mustard and lemon juice in a bowl and mash it all together until the anchovies are basically a slurry or paste. Add the parsley, garlic, chives, capers and red pepper flakes and mix well. Mixing all the while, slowly pour in the olive oil until the sauce comes together. It should look like a very loose pesto or a thick chimichurri. Add salt and black pepper to taste, cover and leave at room temperature.
When the halibut is ready, remove it from the brine and pat it dry with paper towels. Set the halibut out on a cutting board for 15 to 20 minutes to warm up a bit.
Spread some salsa verde on everyone's plate.
Heat the olive oil in a saute pan large enough to fit all the pieces of halibut in one layer. When the oil is hot, pat the halibut dry one more time and lay the pieces in the hot oil. Cook at a medium sizzle (think about how bacon sizzles and you have the right idea) until a nice crust forms on the bottom, about 8 to 10 minutes. Baste the halibut with the hot oil as it cooks for at least 30 seconds, and longer if you want the interior of the fish to be fully cooked through. After about 8 minutes, a crust should form on the bottom of the halibut. Carefully lift the halibut up (assume it will have stuck, although it usually sticks in one one small place, if at all) and place it, crust side up, in the middle of the salsa verde. Serve at once.