Bring a large pot of generously salted water to a boil. Cook the fettuccine according to package directions until al dente — you want a slight bite to the noodle since it will continue to soften when tossed with the hot sauce. Before draining, scoop out about 1/2 cup of the starchy pasta water and set it aside. Drain the fettuccine and keep it ready.
While the pasta is cooking, melt the butter in a large saucepan over medium heat. Add the minced garlic and cook for about 1 minute, stirring constantly, until fragrant. Be careful not to let the garlic brown — browned garlic turns bitter and will throw off the flavor of the entire sauce.
Whisk the flour into the butter and garlic mixture. Cook for about 1 minute, stirring continuously, until the raw flour smell disappears and the mixture turns a very light golden color. This thin roux is what gives the sauce its smooth, velvety body.
Slowly pour in the heavy cream in small splashes, whisking continuously after each addition to prevent lumps. Then add the milk in the same gradual manner. Bring the sauce to a gentle simmer and cook for 3-4 minutes, whisking frequently, until it thickens and coats the back of a spoon.
Reduce the heat to low — this is critical. Adding cheese to a sauce that's too hot will make it grainy and stringy. Sprinkle in the Parmesan and Romano cheese one handful at a time, stirring gently until each addition is completely melted. Once all the cheese is incorporated, stir in the nutmeg, salt, and pepper. Remove from heat.
Add the drained fettuccine directly to the sauce and toss with tongs until every strand is coated. If the sauce is too thick, add the reserved pasta water one tablespoon at a time. Serve immediately topped with extra grated Parmesan, cracked black pepper, and fresh chopped parsley.