Combine sour cream, olive oil, mozzarella torn into small pieces, and ajvar in a food processor. Season with salt and pepper. Blend until smooth but not runny, about 1 minute.
Spread the mixture evenly over the puff pastry. Starting from a long edge, roll the pastry tightly into a spiral log.
Cut the rolled pastry into slices about 1.5 cm thick. Place them cut-side up on a baking sheet.
Bake in a preheated oven at 220°C (425°F) for 20-25 minutes, until the snails are light golden brown.