Place the avocado, garlic, shallots, basil, lemon juice, and salt in a large food processor. Turn the food processor on and slowly stream in the olive oil.
Blitz the avocado mixture until very smooth. Pour the sauce over the rinsed linguine and toss to coat.Taste and season with additional salt if desired.
Transfer the pasta to a platter and top with tomatoes, strawberries, cucumber, and bocconcini. Finish with a sprinkling of gochugaru and additional fresh basil leaves if desired.