Bring a large pot of salted water to a boil. Prepare kale by trimming stems, cleaning and cooking in boiling water for about 4 minutes, or until tender. Drain kale and allow to cool, then squeeze out to dry. Rough chop, and set aside.
In a saucepan, heat 2 tablespoons of olive oil on a medium setting. Add 1 clove of smashed garlic. Flavor oil with garlic, cooking for about 2 minutes until garlic begins to turn golden. Discard garlic. Add breadcrumbs and toast, stirring frequently, until golden brown, about 8 minutes. Transfer breadcrumbs to a separate dish.
Bring a large pot of salted water to a boil for pasta. Cook pasta according to package instructions. Once al dente, drain, reserving 1/2 cup pasta water.
In the meantime, using the same saucepan, warm 2 tablespoons of olive oil over medium-low heat. Add anchovies, red pepper flakes and 2 cloves of chopped garlic. While cooking, mash anchovies with a spoon until they dissolve into the oil, about 2 minutes. Add kale and cook until kale is warmed through, about 5 minutes. Salt and pepper to taste.
Add hot pasta and 1/2 cup reserved pasta water, if necessary, to loosen sauce. Stir to combine. Cook together for 2 minutes to marry flavors. Stir in the Parmesan cheese. Serve topped with toasted breadcrumbs.