Bring a large pot of salted water to a boil. Place a large bowl of ice water next to the pot.
Once the water is boiling, add the spinach. Cook until wilted, about 2 minutes. Use tongs to immediately remove the spinach from the boiling water and into the bowl of ice water. Once cool enough to handle, drain and squeeze well of excess moisture. Transfer to a food processor. Add the eggs, nutmeg, and salt, then process until finely chopped. Pour in the flour and continue to process until thickened and smooth. Transfer the batter to a bowl and cover with plastic wrap. Allow to rest for 30 minutes.
Line a large baking sheet with parchment. Fill the large pot with salted water again and bring to a boil over medium high heat.
Place some of the dough into a spätzle press or colander with large holes and press into the simmering water. Remove using a strainer and transfer to the prepared baking sheet in as much of a single layer as possible. Repeat with remaining batches of dough. Allow to cool while you prepare the sauce.
In a large pan, heat the butter and sage over medium heat. Once the butter has melted, add the speck, tossing to coat. Heat through and remove from heat. Toss in the cooked spätzli and season with salt and pepper.
Serve immediately topped with Parmigiano-Reggiano cheese.