Place all ingredients in a food processor or blender, starting with the liquids and soft ingredients. Pulse for a few seconds, the end result should be a chunky sauce with some texture. Taste and adjust seasoning if needed. Keep on the side until needed. Note: you can make Romesco sauce one day in advance, just keep refrigerated until needed.
To clean the fish: Place fish on a cutting board, feel behind the gills of the fish for the boney plate that gives it its structure. Slide your knife beneath the gill plate, cutting toward the head, when the blade reaches the backbone, turn it and reinsert it so it lays flat, parallel to the backbone, and pointing toward the tail. Draw your knife to the tail in long strokes and stop two inches before the end of the tail. Flip the fish and do the same again on the other side. Use the shears to snip the backbone near the tail and lift it out of the fish. Fish fillets will be united only by the end of the tail.
To cook the fish: Pre-heat oven to 350F. Pat dry fish with paper towels. The drying part is critical, otherwise, the skin won’t crisp. Brush the skinless sides of the fish with romesco sauce then put the skinless sides together and allow to marinade for a couple of minutes.
Set a heavy cast iron over medium-high heat until very hot but not smoky, about 3 minutes. Season skin sides of the fish fillet with salt and black pepper. When the skillet is hot, carefully add 3 tablespoons of olive oil and evenly coat the skillet. Wait a few seconds for the oil to heat then quickly add the fish, skin side down, keeping the skinless filets touching one another. Cook until you can see a golden-brown color on the edge of the skin and the edges of the fish flesh become opaque, 3 to 4 minutes. Carefully and gently use a spatula to lift up the fish and flip it over. Place in the oven and cook for 5 minutes or until fish is completely cooked.
While fish is in the oven, preheat a skillet over medium-high heat and add remaining 1/2 tablespoons of olive oil and heat. Add garlic and cook for a few seconds; add piquillo peppers and thyme, cook until peppers start looking charred, approximately 30 seconds. And mushrooms, season with salt and pepper and cook for 2 to 3 minutes or until mushrooms are cooked. Remove from the pan and place on the side. Return pan to the heat and allow to heat for a few seconds. Add lemon wedges and roast each side just for a few seconds.
Once fish is ready, remove from the oven and place on a large plate. Add cooked vegetables over the fish, garnish with roasted lemon wedges. Optional: you can add more Romesco sauce. Enjoy!