In a large skillet over medium-high heat, toast the walnuts until they just begin to brown, then remove from heat. Place walnuts in a bowl and reserve. Place skillet back over heat and melt the butter, add the garlic and cook until just softened, about 2 minutes. Add milk and bring to a simmer. Then add bread and remove from heat. Stir bread into milk mixture and mash with a spatula until you get a thick paste. Add half the reserved walnuts and the parmesan cheese and, using a hand blender, blend until the large chunks are gone but the sauce still has a coarse texture, then season to taste with salt and pepper.

Cook pasta according to directions on package, reserving ½ cup cooking liquid. Then drain pasta and add it to the sauce. If needed, add some reserved pasta cooking liquid to loosen the pasta. Adjust seasoning, if necessary, and top with remaining walnuts and serve.