Bring a large pot of water to a boil with the 4 halved garlic cloves. Cook the noodles according to the package directions and drain well. Discard the garlic
Melt the butter with the scallions, ginger and 5 cloves finely chopped garlic in a large skillet over medium heat. Add the flour and cook, whisking, until the flour turns light brown, about 3 minutes. Slowly pour in 1 1/2 cups water and stir until a loose gravy consistency; add up to a 1/2 cup more water if necessary. Add the Parmesan and stir to combine. Add the noodles to the sauce and toss to coat well. Add the cilantro and transfer to a serving platter.