Puree the kale, garlic, oil and water with the lime zest and lime juice, season with salt, stir in the cheese.
Cook the kale in boiling salted water for approx. 10 mins., add the spaghettini, cook until just al dente, set aside approx. 150 ml of cooking water, drain the spaghettini. Mix the reserved cooking water with the pesto, return to the pan along with the spaghettini, mix.
Bring the water and vinegar to the boil, reduce the heat. Crack the eggs one at a time and carefully slide into the simmering water, poach for approx. 4 mins. Remove, drain, serve with the spaghettini, season.