Heat the olive oil in a large skillet over medium-high heat. Add the garlic and cook for a few seconds, until fragrant. Add the zucchini and season with salt and pepper. Cover, lower the heat to medium, add cook for 6 minutes, until slightly softened. Remove the lid and cook for another 5 to 6 minutes, stirring gently from time to time, until the rounds are tender but still retain their shape, and most of the juices have evaporated.
While the zucchini is cooking, combine the breadcrumbs, butter, Parmesan, and thyme in a medium mixing bowl. Rub with the tips of your fingers until the mixture resembles coarse meal. (The zucchini and the crumble mixture can be prepared up to a day ahead and refrigerated in separate airtight containers).
Preheat the oven to 400°F Arrange the zucchini over the bottom of a large baking dish. Thinly slice the mozzarella and pat dry with paper towels. Arrange the cheese and figs over the zucchini. Sprinkle the crumble mixture over the dish and bake for 20 minutes, until heated through and golden. Serve warm or at room temperature.