Add anchovies; mash in pan to form a paste. Stir in tomatoes and next 4 ingredients (through pepper); cook 5 minutes, stirring occasionally.
Bring 6 quarts water to a boil.
Add pasta; cook 8 minutes or until almost al dente.
Drain in a colander over a bowl, reserving 1/2 cup pasta water.
Add pasta and reserved pasta water to tomato mixture; increase heat to medium-high. Cook 5 minutes or until pasta is al dente, tossing to combine. Spoon 1 1/2 cups pasta into each of 4 bowls.
Drizzle each serving with 3/4 teaspoon oil; sprinkle with cheese.