Bring a medium pot of water to a boil. Roughly chop the spinach, discarding any big stems, and put it into the boiling water. Cook for 3 minutes, then drain in a colander and set aside to cool. Press out as much extra moisture as possible, and finely chop the pile of cooked greens on a chopping board.
In a large bowl, gently stir together the spinach, ricotta, Parmesan, egg and butter. Season with nutmeg, salt and pepper. Gently stir in the flour, being careful not to overwork it, and set aside for 10-15 minutes.
Meanwhile, melt the 1/4 cup butter in a small saucepan set over medium-high heat. Continue cooking after it melts; it will foam, then turn golden and nutty. Remove from the heat and set aside. Bring a medium pot of salted water to a simmer.
Use two medium spoons to shape the dough into quenelles (small tapered ovals) by scraping about half a spoonful back and forth between the spoons. Place on a floured surface and shake a little extra flour overtop. Gently drop a few gnudi at a time into the simmering water, ensuring that it doesn’t reach a rolling boil, which could break apart the delicate dumplings. Cook for a few minutes, or until they float to the top; at this point you can remove them with a slotted spoon and set aside on a plate.
Serve the gnudi immediately, drizzled with browned butter, with extra Parmesan cheese passed at the table.