Put a large pan of salted water on to boil. Trim the roots and top 4cm off the green garlic bulb. Halve it, then roughly chop the bulb and green stalk. Scoop them into a blender or small food processor (no blender or processor? See our tip below on how to make the pesto the gadget-free way). Pick the leaves off the basil stalks and add them to the blender. Tip in the pine nuts and breadcrumbs.
Add a pinch of salt to the blender and pour in 6 tbsp olive oil and 100ml cold water. Blitz till you have a smooth pesto. Taste and add a little more olive oil, water or salt if you think it needs it, blitzing again to mix. Scoop the pesto into a bowl and set aside.
Scrub the new potatoes and slice them into 1cm-thick slices. Trim the ends off the flat beans and finely slice them on the diagonal.
When the water in the pan is boiling, add the new potatoes. Cover, bring back to the boil then turn the heat down a little and simmer for 5 mins.
Take the lid off the pan. Add the spaghetti to the pan, turn the heat up and simmer for 5 mins. Drop the flat beans into the pan and simmer for another 5 mins. The potatoes should be tender when pierced with a fork, and the spaghetti and flat beans tender but still with a little bite.
Scoop 1 cup water out of the pan (mind your fingers) and set aside. Drain the spaghetti, potatoes and beans. Tip them back into the pan and set over a medium heat. Add half the pesto to the pan with 2 tbsp of the pasta water. Toss to mix everything together and warm through. Add a little more pesto or water if you think it needs it.
Divide the spaghetti between 2 warm plates, top with handfuls of the rocket and drizzle with 1 tbsp balsamic vinegar to serve.