Put ricotta in a cheesecloth-lined strainer set over a bowl and let drain overnight in refrigerator. Measure 1 1⁄4 cups drained ricotta and reserve any remaining ricotta for another use.
Bring a large pot of salted water to a boil and add chard; cook until soft, 3-4 minutes. Drain chard and let cool. Squeeze chard with your hands to expel liquid. Transfer chard to center of a tea towel, bring up edges, and squeeze to expel remaining liquid. (Alternatively, working in batches, put chard in a potato ricer and squeeze to expel liquid.) Transfer chard to a food processor and pulse until finely chopped. Transfer chard to a large bowl along with drained ricotta, 1 tsp. salt, 8 tbsp. butter, flour, nutmeg, egg yolks, and egg. Season with pepper and mix until smooth. (Test 1 dumpling: Bring a small pot of water to a boil. Measure out 1 tbsp. of mixture, roll in flour, and boil until the dumpling floats. If dumpling falls apart, stir 1⁄4 cup more flour into mixture.)
Using a spoon, divide mixture into about 40 portions. Working with 1 portion at a time, use 2 spoons to shape portion into an oval and dust with flour. Transfer dumplings to a lightly floured baking sheet and repeat with remaining portions. (If not cooking immediately, cover and freeze malfatti for up to 6 months.)
Bring a large pot of salted water to a boil and add dumplings; cook until dumplings float, 1-2 minutes. Using a slotted spoon, transfer dumplings to a baking sheet. Meanwhile, heat remaining butter in a 10" skillet over medium-high heat, stirring occasionally, until lightly browned, about 5 minutes. Add sage and cook until leaves are crisp, 1 minute. Divide dumplings between 6 serving plates, drizzle with sage butter, and garnish with more Parmesan and nutmeg, if you like.