Place sun-dried tomatoes in a heatproof bowl. Cover the tomatoes with boiling water, then cover the bowl with a plate and let sit for 15 minutes. This will help to soften the tomatoes.

Drain tomatoes and place in the bowl of a food processor. Add lemon juice and zest, garlic, kalamata olives, green olives, parsley and basil. Pulse the mixture 10 to 12 times, until the olives and tomatoes are broken down. With the machine running, stream in olive oil and process until the mixture resembles a chunky pesto.

Serve with bread, pita, or crackers. Any leftovers will stay fresh in an airtight container in the fridge for up to 5 days.