Heat a large sauté pan over medium-low heat, add the olive oil, red pepper, garlic and anchovy and cook, stirring occasionally, until the anchovies dissolve and the mixture is fragrant, about 5 minutes. Remove from the heat and set aside.
Meanwhile, bring a large pot of salted water to a rolling boil over medium heat. Add the rapini and cook until bright green and softened, about 30 seconds to 1 minute. Using tongs, transfer to a colander and rinse under cold water. Drain and set aside.
Return the pot of water to a boil. Add the spaghetti and cook, stirring occasionally, until al dente, about 10 minutes. Drain and return the pasta to the pot. Add the sauce and cooked chard and toss to combine.
Heat a medium sauté pan over medium-low heat, add the butter and allow to melt. Add the breadcrumbs and stir to evenly combine with the butter. Let cook, stirring occasionally until the breadcrumbs are golden brown, about 2 minutes. Remove to a small bowl and stir together with the lemon zest.
Divide the pasta among warmed bowls and top with the breadcrumb mixture and cheese.