In a large pot of boiling salted water, cook pasta until al dente according to package directions. Reserve 1 cup pasta water before draining.
Meanwhile, in a large skillet over medium-high heat, heat 3 tablespoons oil. Add minced garlic and bread crumbs and season with red pepper flakes and salt. Cook until bread crumbs are golden and garlic is fragrant, about 3 minutes. Transfer bread crumbs to a paper towel–lined plate and wipe out skillet.
Return skillet to medium heat and add remaining 1 tablespoon oil and butter. When butter is melted, add sliced garlic and anchovies, if using. Cook until garlic is fragrant and anchovies are dissolved, about 2 minutes.
Add pasta to skillet and toss to combine. Stir in lemon zest and juice. And 1/2 cup pasta water and toss, adding more as needed to thicken sauce. Stir in parsley and three-quarters of the bread crumbs and toss to combine.