Preheat oven to 550 degrees. Cut the mushroom caps in half, then cut them across into 1/8-inch wide slices. Set aside. Line 2 large baking sheets with parchment paper and grease the paper with olive oil. Cut off the thin tail section of each cod fillet and place 1 fillet on each baking sheet, on the diagonal, if necessary, to make them fit. Season the cod with salt and pepper and sprinkle with the rosemary and thyme. Make alternating rows of chorizo, tomato, and mushroom slices across each fillet until the cod is completely covered. Scatter the garlic over the fish, then sprinkle it generously with cayenne. Sprinkle the parsley and scallions over the fillets and season with salt. Place the lemon slices down the center of each fillet and drizzle olive oil over all. (The recipe can be made to this point up to 2 hours ahead: refrigerate). Roast the cod for about 25 minutes until cooked through, spooning the oil that accumulates on the baking sheet over the fish from time to time. Halfway through the cooking, switch the positions of the baking sheets in the oven. To check for doneness, insert a skewer into the center of the fish for 5 seconds. The fish is done when the skewer goes in easily and then feels hot when touched to your lip. Spoon the oil on the baking sheet over the fish and squeeze the juice of 1/2 lemon over each fillet. Slide the cod, with the parchment, onto 2 large serving platters.