For tomatoes, cut off the tops and a thin layer from the bottom so that they stand firmly on the dish. Remove the inner pulp and juice from the tomatoes through the uppercut part.
Cover the baking sheet with paper towels and put the tomatoes on them to glass the liquid, leave for 30 minutes at room temperature.
Meanwhile, prepare the filling. Put the avocado, cream cheese, pesto sauce and lemon juice into the bowl of a kitchen processor, pulsate until smooth. Place the filling in a piping bag with a narrow nozzle.
Place dried tomatoes on a serving dish, cut top up, and fill the tomatoes with the filling from the bag. Sprinkle small basil leaves on the stuffed cherry tomatoes, if desired. Serve the stuffed tomatoes immediately, or chill in the refrigerator for 2-4 hours.