Prepare the Marinade: In a medium bowl, whisk together the extra virgin olive oil, white wine vinegar, and chopped fresh parsley.
Marinate the Hearts of Palm: Drain, rinse, and slice the hearts of palm into ¼-inch (6mm) rounds.
Add them to the marinade, season with salt and pepper, then toss gently to coat.
Cover and chill for at least 2 hours, or overnight for best results.
Prepare the Tomato Cups: Slice each tomato in half crosswise. Use a small spoon or melon baller to carefully scoop out the inner pulp and seeds, creating 20 hollow tomato shells. Save the pulp for another use, like a sauce or soup.
Season and Fill: Lightly sprinkle the inside of each tomato shell with a pinch of salt and pepper. Give the marinated hearts of palm a final stir, then divide the mixture evenly among the 20 tomato shells, mounding it attractively in each one.
Serve: Arrange the stuffed tomatoes on a serving platter and serve immediately for the best texture and flavor.