Bring a large pot of water to a boil. Liberally salt the water and cook linguine to al dente.
While the pasta cooks, heat 2 tablespoons olive oil in a large skillet over medium-high heat. Once the pan is hot, add zucchini and yellow squash noodles and cook until brown, about 3-4 minutes. Add anchovies and cook until they begin to break up, about 3-4 minutes.