Combine all —artichoke hearts, roasted red peppers, garlic, lemon zest and juice, capers, cilantro, basil, olive oil, salt, and pepper—in the bowl of a food processor.
Pulse-blend a few times until the are roughly chopped.
Scrape down the sides of the bowl with a spatula.
Process continuously until the dip is well-blended but still retains a chunky, rustic texture.
Transfer the dip to a serving bowl.
Serve immediately with fresh veggies, crackers, or toasted baguette slices, or use as a sandwich spread.
Don't over-blend! The beauty of this dip is its chunky, rustic texture. Pulse the food processor and check frequently to avoid turning it into a smooth purée.