Pour the vegetable stock into a saucepan and season lightly with salt, taking care not to add too much as the stock will later be boiled and reduced.
Bring to the boil, add the baby onions and cook for 15–20 minutes, or until they are just tender.
Meanwhile, peel the cucumbers, cut them in half lengthways, remove the seeds with a teaspoon and cut the flesh into thick slices. Add the cucumbers and shredded basil to the onions and cook for 10 minutes, or until the cucumbers are just cooked through. Be careful not to overcook.
Drain the cucumbers and onions, reserving the stock, and put the vegetables in a serving dish. Keep warm. Boil the reserved stock rapidly until it is reduced to about 3 tablespoons. Stir in the butter and heat gently. Spoon this sauce over the cucumbers and onions, garnish with a sprig of basil and serve.