Italian Puttanesca

6 tablespoons (90ml) extra-virgin olive oil, divided
4 medium garlic cloves, thinly sliced or finely chopped by hand (see notes)
4 to 6 anchovy fillets, finely chopped (1 ½ to 2 tablespoons)
Large pinch red pepper flakes
¼ cup capers, drained and chopped (about 2 ounces; 60g) (see notes)
¼ cup chopped pitted black olives (about 2 ounces; 60g) (see notes)
1 cup (225g) whole peeled tomatoes, preferably San Marzano, roughly broken up by hand (about half a 14-ounce can)
One 5-ounce (140g) can oil-packed tuna (optional)
Kosher salt
8 ounces dried spaghetti
Small handful minced fresh parsley leaves
1 ounce (30g) finely grated Pecorino Romano or Parmesan cheese, plus more for serving
¼ teaspoon freshly ground black pepper

In a medium skillet, combine 4 tablespoons (60ml) oil, garlic, anchovies, and red pepper flakes. Cook over medium heat until garlic is very lightly golden, about 5 minutes. (Adjust heat as necessary to keep it gently sizzling.) Add capers and olives and stir to combine.
Add tomatoes, stir to combine, and bring to a bare simmer. If using, stir in canned tuna, flaking it gently with a fork. Remove from heat.
Using tongs, transfer pasta to sauce. Alternatively, drain pasta through a colander, reserving 1 cup of the cooking water. Add drained pasta to sauce.
Add a few tablespoons of pasta water to sauce and set over medium-high heat to bring pasta and sauce to a vigorous simmer. Cook, stirring and shaking the pan and adding more pasta water as necessary to keep sauce loose, until pasta is perfectly al dente, 1 to 2 minutes longer. (The pasta will cook more slowly in the sauce than it did in the water.)
Remove from heat and stir in remaining olive oil, parsley, and cheese. Season with salt and pepper (be generous with the pepper and scant with the salt—the dish will be plenty salty from the other ingredients). Serve immediately with more grated cheese at the table.