Cook the potatoes in unsalted boiling water. Do not peel the potatoes beforehand or pierce the skins in any way with a fork. When the potatoes are done (soft and crumbly, but dry), drain them and allow them to cool slightly.
Whilst the potatoes are cooking, prepare the pesto. Blanch the peas in salted water and drain as soon as the water begins to boil; quench them in a bowl of iced water and drain. Combine all the pesto ingredients together in a food processor or blender; blitz together until a smooth creamy pesto is formed. Set the pesto to one side and continue preparing the potatoes.
Skin the potatoes whilst still hot and then place them in a bowl or onto a chopping board covered with baking parchment. Crush the potatoes using either a fork or a potato ricer.
When the potatoes have stopped steaming, add the grated lemon peel, flour and salt.
Knead the mixture with your hands. The quantity of flour stipulated in the recipe should be sufficient. However, depending on the quality of the potatoes and upon their cooking time, it may be necessary to carefully add a little more flour.
Shape the potato mixture into a ball and allow it to rest for a few minutes. Dust a pastry board with flour, cut the ball of potato mixture into slices and form them into rolls of about 1.5 cm in width. Cut each roll into equal-sized chunks or cubes to form your gnocchi. Lightly dust these with flour, handling them as little as possible.
Cook the gnocchi (a few at a time), together with the peas, in boiling salted water for about 1 minute (i.e. until the gnocchi rise to the surface). Remove with a slotted spoon, drain well and place into a non-stick pan or casserole dish.
Add the pesto and gently combine utilising the residual heat alone (if you need to stir, do so very carefully).