Cook the spaghetti according to package instructions - adding 100g of the peas 3 minutes before the end of the cooking time. Drain and keep warm in the pan.
Meanwhile, slice the bacon into small cubes or strips, then fry or grill until crispy. Set aside.
Blanch the remaining peas in boiling water, for about 5 minutes. Drain, but put aside about a cupful of the cooking water.
Put the peas back into the pan, add the oil, garlic, lemon juice and mint leaves then, using a hand-held blender, purée it. Stir in the grated cheese, season to taste.
Toss the pasta and peas with the pea purée, then add the bacon. If the pasta is too dry, stir through a few spoonful of the reserved cooking water. It should be moist but not too wet!
Serve with ground black pepper and perhaps with more grated cheese on top.