Heat oven to 400 degrees. To prepare tuna packets: Cut parchment packets, as described above. In each packet, place 2-4 lemon slices, 4-5 slices bell pepper, 4-5 slices red onion, about ¼ cup cherry tomatoes and tuna steak. Drizzle with 1 tablespoon broth or wine, 1 teaspoon olive oil and season with salt and pepper. Top with basil leaves and then fold to seal. Repeat with remaining packets.
Place packets on a baking sheet and bake in a 400 degree oven for 15-20 minutes, depending on the desired doneness: 14-15 minutes for medium-rate, 16-18 minutes for medium or 18-20 minutes for well.
While fish bakes, prepare salsa verde. Place all ingredients, except for oil in a food processor and pulse until finely chopped. With processor running, drizzle in olive oil to desired thickness. Season to taste and add additional vinegar or oil to flavor to your liking, if desired.
When fish is done, remove each packet to a plate. Cut or tear open packets tableside and serve immediately with a drizzle of salsa verde and lemon wedges.
To make up to four hours ahead: Prepare packets as described and refrigerate. When ready to serve, remove from fridge, place on a baking tray and bake according to above directions.