Preheat the oven to 375F. In a large bowl toss the cherry tomatoes, garlic, smoked paprika, chorizo, shallot, olive oil, and vinegar.
Season the fish with salt and pepper the place on one side of the parchment paper. Top with half of the tomato-chorizo mixture. Working from one end, begin tightly folding and crimping the open edge of the paper until the packet is sealed. Repeat this process with the second piece of fish.
Place the parchment packets on a baking tray and bake for 12-15 minutes. If the fish is on the thin side start with 12 minutes if its thicker go for 15.
Serve the fish in its parchment, for an impressive presentation! Top with chopped parsley and lemon slices.