Bring water to a boil. Add salt and 1 lb. new potatoes. Boil for 10-15 minutes. When the spuds are easily pierced with a knife but have not “exploded”, drain them and immediately cool in a bath of cold water.
Lie 1 medium or 2 small zucchini on a cutting board. Use a vegetable peeler to shave off very thin slices the full width of the squash. Cut the slices in half widthwise.
Place the shaved squash in a bowl and sprinkle with salt. Allow to sit for 5 minutes, then toss and sprinkle with the juice of 1/2 a lemon.
In a small skillet, saute 4 minced cloves of garlic and 2 T. minced fresh rosemary in 4 T. olive oil over low heat until the garlic is soft but not brown. Use a mortar and pestle (or small food chopper) to mash everything into a rough pesto. Season with salt.
Toss the potatoes with the pesto to coat, then add the squash. Season with salt and pepper. Add grated parmesan cheese if you like.