In the bowl of a food processor, process the breadcrumbs until finely ground and set aside.
Prepare and ice bath by filling a large bowl with ice and cold water. Bring a large pot filled generously salted with water to a boil over medium-high heat. Add the spinach and blanch until wilted, about 2 minutes. Remove immediately from the pot with tongs and transfer to the ice bath. When cool, drain the spinach into a colander. Place the spinach in a kitchen towel and wring until mostly dry.
Finely chop the spinach and place in a medium bowl. Add the egg, the salt and pepper, a few swipes of nutmeg, the pecorino cheese, and the breadcrumbs and mix with your hands until just combined. Add the flour and gently knead until combined.
Line a baking sheet with parchment paper and lightly dust with flour. Put about 70 g (1/2 cup) flour in a shallow bowl. Using two large spoons, scoop enough dough to make a dumpling a little smaller than a golf ball. With your hands, gently roll the dough into a compact ball and roll in the flour to coat. Put the strangolapreti on the prepared baking sheet and shape the remaining dumplings.
When all the strangolapreti are formed, shake the baking sheet to roll the pasta around in the flour to evenly coat. Refrigerate uncovered for at least an hour.
Bring a large pot of generously salted water to a simmer over medium, high heat. Add the strangolapreti and simmer until tender, 1 to 3 minutes. They will not float.
Remove immediately with a slotted spoon and divide among four bowls. Finish with melted butter and a grating of Parmigiano-Reggiano cheese.