Pour olive oil into a 12-inch frying pan or 14-inch wok over medium-high heat. Add green beans and stir often until tender-crisp and lightly browned, 10 to 12 minutes. Add garlic and stir just until fragrant, 1 minute.
Add wine, lime juice, and salt and pepper to taste; stir until liquid boils, 1 minute. Pour into a serving dish and sprinkle with Manchego cheese. Serve hot.