Pile flat-leaf parsley leaves on a cutting board and chop finely until pieces measure about 3-4mm, roughly the size of a grain of rice. Transfer to a mixing bowl.
1 cup flat-leaf parsley
Rinse capers under cold water for 10 seconds to remove excess brine. Roughly chop green olives into 5mm chunks and mince garlic into 2mm pieces. Add all to the bowl with parsley.
½ cup green olives, 2 tablespoons capers, 1 clove garlic
If using, mince anchovy fillets and add them along with red pepper flakes, black pepper, and fresh lemon juice. Stir everything together thoroughly with a fork for 30 seconds.
1 teaspoon anchovy fillets, ¼ teaspoon red pepper flakes, ¼ teaspoon black pepper, 1 tablespoon lemon juice
Pour extra-virgin olive oil in a thin, steady stream while whisking constantly for about 1 minute until the sauce looks glossy and slightly thickened instead of separated.
⅓ cup extra-virgin olive oil
Let the salsa sit at room temperature for 10-15 minutes so the garlic mellows and all flavors meld. Taste and adjust seasoning with more lemon juice or salt if needed before serving.