Parboil green beans in a pot of salted, boiling water for about 3 minutes, or until just slightly tender. Strain and place beans in bowl of cold water to keep beans from cooking further and to bring them to room temperature.
On a large serving platter, cover bottom with a layer of green beans. Then place the tomato slices in a single layer on top. Cover each tomato with a thin slice of mozzarella. Sprinkle the minced garlic and chopped basil on top.
In a small container, mix the olive oil, balsamic vinegar, and salt until combined. Drizzle over the salad and serve.