In a large sauté pan, heat the oil from one of the jars of tuna and sauté the red onion until slightly soft and translucent, 3–5 minutes. Add the mushrooms and cook until the mushrooms are soft and slightly browned, about 5 minutes. Then, add the red peppers, green olives, sun-dried tomatoes and capers and cook for 1 minute on high. Turn the heat off and reserve the mixture for assembly.
Cook the pasta in boiling water according to the package instructions. Then, drain the pasta, add it back to the pot with 1 tablespoon of the oil from the other jar of tuna and set it to the side.
To make the avocado sauce, combine all of the sauce ingredients in the bowl of a food processor and pulse on high until the ingredients are finely chopped. With the motor running, add the oil from one of the jars of tuna in a slow stream until the mixture is emulsified. Taste and adjust the seasonings by adding more anchovy paste, black pepper or lemon.
Fold the sauce gently into the pasta mixture. Flake the tuna and toss it, along with the veggie mixture, with the sauced pasta and garnish as desired.