Cut the stem end off each tomato with the serrated knife. Slice crosswise into 1/4 inch rounds, about 14 slices that hold together when lifted.

Lay the tomato slices in one layer on the lined sheet pan and sprinkle with the fine sea salt. Rest for 10 minutes, until beads of juice show on top and the towel looks damp.

Slice each mozzarella ball into 1/4 inch rounds with the thin knife, wiping the blade after every cut. Aim for about 14 slices with smooth edges.

Blot the tomato slices lightly with a fresh paper towel. Arrange tomatoes and mozzarella on the platter in overlapping rows, each slice overlapping the next by about one third, and tuck half the basil between the slices.

Spoon the olive oil over the slices and grind the pepper on top, until the oil shines on the tomatoes.

Tear the remaining basil over the platter and drizzle the glaze in thin zigzag lines. Serve within 15 minutes, while the glaze still sits in dark lines on the white cheese.