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Prepare an ice bath. Fill a large bowl halfway with ice cubes and add some cold water. Put a colander squarely inside the ice bath. The colander will keep you from having to pick the peas out from amongst the ice cubes in the ice bath. Bring a large pot of water to a boil over medium heat. Add salt until the water tastes like seawater, then add a generous pinch of sugar. Add the snow peas and cook until they are bright green and tender, about 1 to 2 minutes. Remove the peas from the water with a strainer and transfer them to the colander inside the ice bath. Allow them to sit until cooled. Drain on a kitchen towel-lined plate.
Bring the water back up to a boil and add the shelled peas. Cook until the water comes back to a boil, about 1 minute. Use the strainer to remove the peas and plunge them into the colander/ice bath. Allow them to sit in the ice water to assure they have cooled thoroughly. Discard the blanching water.
Remove the peas from the ice bath and spread them out onto the kitchen towel over flat surface. Use another kitchen towel to gently pat them dry. Transfer the towel to a plate and put the peas into the refrigerator to chill until you are ready to serve.
Transfer the chilled shelled peas, snow peas and raw sugar snap peas to a medium bowl. Stir to blend. Toss with the vinaigrette, basil leaves and pea shoots and season with salt, to taste. Add more seasoning, if needed. Transfer the salad to a platter and serve immediately.