Open and drain the 2 (14.5-ounce) cans of green beans; drain well (you may rinse and drain again if desired).
Heat a large skillet over medium heat. Add 1 tablespoon butter and 2 teaspoons olive oil and heat until the butter is melted.
Add 4 cloves thinly sliced garlic to the skillet and sauté, stirring, about 1 minute, until fragrant and just beginning to soften (do not let it brown).
Add the drained green beans to the skillet, season with salt and pepper to taste, and toss to coat with the garlic-butter-oil.
Cook, stirring or tossing occasionally, until the beans are heated through and slightly tender, about 6–8 minutes.
Remove the skillet from the heat, sprinkle 1/3 cup shredded Parmesan cheese over the beans, gently toss to combine, and serve immediately.