Preheat the oven to 425°F. Line a large baking sheet with parchment paper.
Pat the chickpeas thoroughly dry with a clean kitchen towel, removing any loose skins. Spread them on the baking sheet and toss with the olive oil, oregano, salt, and garlic powder.
Spread into a single layer and roast for 30-35 minutes, shaking the pan halfway through, until golden and crisp. Let cool slightly; they will crisp up more as they cool.
Add the vegan mayonnaise, capers, caper brine, garlic, Dijon mustard, lemon juice, salt, and pepper to a small food processor or blender. Blend until smooth. Add water, 1 teaspoon at a time, until the dressing reaches your desired consistency. Taste and adjust the seasoning.
Place the romaine in a large bowl. Add the vegan parmesan and enough dressing to lightly coat the leaves, then toss to combine.
Top with the crispy chickpeas and serve immediately, with any remaining dressing on the side.