Slice the shiitake mushrooms as thinly as possible and place in a large bowl. Peel the ginger and thinly slice it. Cut the slices into thin matchsticks and put in a small pan. Pour in 2 tbsp each honey and rice vinegar. Zest in the lime and squeeze in the juice from half of it. Add a good pinch of salt.
Place the pan on a gentle heat. Bring to a gentle simmer, then immediately remove from the heat. Pour the ginger pickling liquor over the shiitake mushrooms. Stir and leave to cook in the pickle liquor.
Pour the sesame seeds into a small pan and toast on a medium heat for 2-3 mins. Tip into a small bowl.
Submerge the radishes with their leaves in water. Give them a good swirl, then drain and pat dry with kitchen paper. Trim the radishes and set the leaves aside. Slice the radishes as thinly as possible. Halve the cucumber and scoop out the seeds with a teaspoon. Discard the seeds and slice the cucumber into thin crescents.
Tip the pickled shiitake mushrooms into a sieve, catching the sweet and sour liquor in a bowl.
Place the pea shoots and radish leaves into a large bowl or on a serving platter. Add the radishes and cucumber with half the sesame seeds. Drizzle over most of the shiitake pickling liquor and toss.
Pile the pickled shiitake mushrooms on top of the salad. Sprinkle over the reserved sesame seeds and spoon over a little of the remaining pickling liquor to serve.