In a small, nonstick skillet, heat the oil over medium-low heat. Add the garlic and cook until fragrant, but not brown, about 30 seconds. Remove the pan from the heat and stir in the rosemary. Set aside.
Combine the edamame beans, cannellini beans, cheese, parsley, and salt and pepper in a serving bowl. Add the garlic mixture and toss well until all the ingredients are coated.