Heat oven to 450º. Halve two heads of garlic crosswise with a knife and brush with 2 T extra-virgin olive oil; wrap with foil. Roast until soft, 1 hour. Let cool and squeeze roasted garlic cloves from their skins into a bowl; mash with a fork to a paste. Add 1/2 c milk, 1/4 c finely chopped flat-leaf parsley leaves, 1/4 t kosher salt, and 3 beaten eggs; stir until smooth. Put 2 c flour into a large bowl; form a well in center. Slowly pour in the garlic-milk mixture, stirring with a fork to form a smooth batter. bring a 5-qt saucepan of salted water to a boil over high heat. Set a perforated spätzle-making disk (or a wide-hole colander) over the pot. Working in batches, scrape batter through holes into water. Cook until dumplings rise to surface, about 1 minute. Heat 4 T unsalted butter in a 12" ovenproof skillet over high heat. Add dumplings; cook, stirring, until lightly browned, 6-8 minutes. Meanwhile, heat broiler; put rack 5" from heating element. Sprinkle dumplings with 1 c grated emmentaler cheese; broil until melted, about 2 minutes.