Cook the potatoes in boiling salted water for approx. 30 mins. until soft. Drain the potatoes, cut in half, allow the residual moisture to evaporate by shaking the pan on the switched-off hob. Push the potatoes through a sieve into a bowl, allow to cool.
Preheat the oven to 60°C, warm the bowls and plates. Blanche the spinach briefly in boiling water, remove using a slotted spoon, cool immediately in ice-cold water, drain the spinach well, puree with the egg, add to the potatoes along with the flour and cheese, mix quickly to create a dough, season. On a lightly floured surface, shape the gnocchi mixture into rolls (each approx. 1.5 cm in diameter), Cut the rolls into pieces approx. 1 cm long, roll them over the prongs of a fork. Cook the gnocchi in batches in gently simmering salted water for approx. 5 mins. until they float to the surface. Remove the gnocchi with a slotted spoon and drain.
Heat the clarified butter in a non-stick frying pan. Fry the gnocchi in portions for approx. 4 mins., stirring occasionally, keep warm. Fry the lettuce in the same pan for approx. 3 mins. Add the spinach and garlic and fry briefly, season with salt. Add the gnocchi, mix carefully.
Serve the gnocchi on the pre-warmed plates. Place the burrata on top, scatter over the Pecorino, season.