Rinse, scrub, and slice the potatoes into 1/2-inch slices.
Place the potatoes in a pot and cover with water, just enough to cover them.
Place over high heat and bring to a boil. Reduce the heat to medium, and allow the potatoes to cook for 8-10 minutes or until they can be pierced easily with a fork. Drain the potatoes and arrange them on a plate.
Heat a grill pan or an outdoor grill to medium-high. Brush the potatoes with the olive oil and place on the grill for 3-5 minutes on each side or until grill marks are achieved. Remove from the heat and arrange the grilled potatoes on a platter.
In a medium-sized bowl, combine the tomatoes, mozzarella, onions and basil. Adjust the seasoning to your liking using salt and pepper. Top each potato plank with a spoonful of the tomato-mozzarella mixture and enjoy!