Fill a pasta pot with an insert with water. Bring to a low boil.
For the gnocchi: Place the bread in the bowl of a food processor and process until fine crumbs form. Transfer to a large bowl and pour in the milk. Let sit for 5 minutes. Whisk the eggs, ricotta, Parmigiano and 1/2 teaspoon kosher salt together in a medium bowl. Stir the egg mixture into the bread mixture. Fold in the flour. The dough will be sticky.
Sprinkle a sheet pan with flour.
Dust a work surface with flour. Divide the dough into 6 portions. Roll a portion into a 1/2-inch-thick log. Using a metal bench scraper or butter knife, cut the log into 1/2-inch pieces. Place on the prepared sheet pan and continue with remaining dough.
For the pistachio pesto: In the bowl of the food processor, combine the pistachios, basil, 1/2 cup of Parmigiano and garlic. Pulse until fine crumbs form. With the food processor running, slowly drizzle in the oil and process until the pesto pulls away from the sides of the bowl. Transfer to a medium bowl, stir in the lemon zest and season with salt.
Season the boiling water with salt. Drop gnocchi into the boiling water and cook for 2 to 3 minutes. (Tip: Once floating, cook an additional 30 seconds and they are done!) Use a slotted spoon or spider to remove the gnocchi and place directly into the bowl with the pesto. Add a ladleful of pasta cooking water to loosen sauce. Swirl the gnocchi around until evenly coated. Place gnocchi on a platter, top with more Parmigiano and stop resisting: Take a bite!