Add the garbanzo beans to a food processor and pulse 5 to 10 times, or until they're chopped and take on a flaky texture. Do not over-process. Transfer to a large serving bowl.
Next, add the artichoke hearts to the food processor. Pulse about 10 times, or until they're chopped and take on a flaky texture. Carefully gather the chopped artichokes within your hands or within a piece of cheesecloth, and press the excess water from them. They don't need to be completely dry, but you want to release any excess liquid to ensure a more "tuna-like" texture. Add to the bowl with the garbanzo beans.
Stir in the red onion, olives, roasted red peppers, sun-dried tomatoes, parsley, capers, vegan mayonnaise, lemon juice, and oregano.
Season to taste with sea salt and black pepper. (Note: depending on how salty your olives, sun-dried tomatoes, etc. are, you may not need to add much salt.)
Serve on its own, tucked into pita bread, or on top of sandwich bread, baguette slices, crackers, cucumber slices, etc.
Cover and refrigerate leftovers for up to 3 days.