Bring a large pot of water to a boil. Boil pierogi and stir occasionally for 5 mins. Drain and place in a bowl.
Add basil, garlic and salt in a mortar. Working with the pestle, press and rotate it, keep going for a few minutes until all the ingredients are finely ground. Add olive oil, stir and set aside
Thread 4 pierogi, 2 tomatoes, and 2 mozzarella balls, onto a bamboo skewer, alternating the ingredients. Repeat with remaining ingredients; this makes 8 skewers.
Place on a board or platter and drizzle with the basil sauce.