In a medium bowl, steep the garlic in the olive oil for 10 minutes.
Meanwhile, in a small saucepan of boiling salted water, cook the green beans until just tender, about 3 minutes. Using a slotted spoon, transfer the beans to a work surface and let cool, then cut into 1-inch lengths. Add the cranberry beans to the boiling water and simmer over moderate heat until tender, about 12 minutes; drain.
Add the hot cranberry beans and the thyme to the olive oil and let steep, stirring a few times, until the beans have cooled, about 10 minutes. Discard the garlic. Add the green beans to the olive oil and season with salt.
Arrange the tomato slices on a platter and season with salt and pepper. Spoon the beans over the tomatoes, sprinkle with the basil and serve.