Melt butter with the oil in a large saucepan over medium-high heat. Cook and stir onion and garlic in the butter mixture until tender, 3 to 5 minutes. Add cucumber and zucchini slices; cook and stir until softened, 2 to 3 minutes. Pour vegetable broth over the mixture; bring to a boil, reduce heat to medium-low, and let simmer until the vegetables are cooked through, 20 to 25 minutes. Remove from heat and cool a few minutes.

Pour soup into a blender no more than half full. Cover and hold lid in place with a towel; pulse a few times before leaving on to blend. Puree in batches until smooth.