Place the garlic, capers, anchovy fillets, lemon zest and lemon juice in the workbowl of a food processor fitted with a chopping blade. Process to a coarse purée, scraping down the sides of the work bowl with a rubber spatula as needed. Add the parsley and mint, and drizzle in the olive oil while running the processor. Scrape down the sides of the work bowl with a rubber spatula and season with salt and freshly ground black pepper to taste. Transfer the salsa verde to a tightly covered container and refrigerate until use