Add both types of pitted olives, roasted red peppers, cauliflower, chopped carrot, chopped celery, pepperoncini and garlic cloves to a food processor and pulse just a few times until the ingredients are chopped into smaller pieces - you want small pieces, not a paste.
Add 2 tablespoons of capers, salt, chili flakes, lemon juice, red wine vinegar, lemon zest, chopped parsley and 3 tablespoons of olive oil. Pulse once just to combine. Add 2 tablespoons more of capers into the olive salad mixture and stir to combine. Taste and adjust seasoning with more salt if desired.
Toast the sourdough (or pita) in a pan with a little olive oil or in a toaster.
Spread the labneh on a large plate or in a shallow bowl. Top with the olive salad and then serve with pieces of toasted sourdough or pita.
Notes
Instead of serving with labneh, you could use plain Greek yogurt or plain cream cheese.
This is lovely served as an appetizer or store in an airtight container in the fridge for up to 5 days.