Heat an oven to 400°F. Pat the fish filets very dry with paper towels, remove any pin bones, if necessary, and season generously with salt and pepper. Set aside.
If using fresh peas in the pod, shell them (you should get a little more than 2 cups.)
Cut the lemon in half crosswise and juice one half; cut the other half into wedges for serving and set aside. Using a Microplane grater, grate ½ the garlic clove into a medium bowl, whisk in 1 tablespoon of the lemon juice, a big pinch of salt, the sugar and some black pepper. While whisking, slowly dribble in 2 tablespoons olive oil to make an emulsified dressing.
Mince the onion or shallot. Melt 2 tablespoons butter in a saucepan and add the onion. Cook, stirring, until fragrant and translucent, 2–3 minutes, then add the fresh (or frozen) peas. Sauté just until warmed through, 3–4 minutes, season with salt and pepper and scrape into a high-speed blender. Add ½ cup water, 1 teaspoon lemon juice and purée until very smooth; set aside and keep warm. (If you don’t have a high-speed blender, purée the peas in a food processor until as smooth as possible.)
Heat remaining butter and 1 tablespoon olive oil in an oven-proof skillet and add the fish fillets. Don’t move them! Let a brown crust form on one side of the fillets, about 4 minutes. Flip the fillets and place the pan in the oven to finish cooking, an additional 4–5 minutes depending on the thickness of the fish. Check with the tip of a knife and when the fish is just barely translucent, remove the pan from the oven, squeeze some lemon juice over the top and set aside to rest, about 2 minutes. While the fish rests, mince the chives.
Toss the herbs and lemon zest with the dressing. Pour the warm pea sauce into the middle of each of 4 plates and nestle a fish fillet in the middle; top with a handful of herb salad and a heavy sprinkle of minced chives. Serve with lemon wedges at the table.