Toast the breadcrumbs in a skillet with a tablespoon of olive oil over medium-high heat. Keep tossing until golden brown and crunchy. Set aside.
Cook the spaghetti according to package instructions in a pot of salted boiling water until al dente.
Sauté garlic, capers, crushed red pepper, and anchovies with the remaining olive oil for a minute over medium heat. Press anchovies against the pan until they disintegrate and blend with the sauce.
Add olives, lemon zest, and lemon juice.
Drain the spaghetti and combine it with the sauce.
Add about ½ cup of pasta water or more as needed. Toss them together until the pasta absorbs most of the sauce. Season with salt and pepper, as desired.
Turn off the heat, then add half of the breadcrumbs.
Toss in some fresh parsley, if using.
Serve immediately to keep the breadcrumbs crunchy. Add more breadcrumbs and parsley as garnish.
Notes
Panko breadcrumbs: Japanese-style breadcrumbs that are flaky and coarse. You can make your own using stale or dry bread and crush them into tiny crumbs.
Capers: Green flower buds that are tangy and salty. The smaller ones, labeled "non-pareil," have a delicate texture and are less acidic than the bigger ones.
Anchovy fillets: These umami-rich fillets are available in cans or jars, salt-cured, and stored in olive oil. Wild Planet or Roland are inexpensive brands you can use. If your anchovies are too salty, use less.
Olives: Choose olives you enjoy eating. If you are unsure what to get, use an assortment. If you don't like olives, use more capers instead.