Preheat Oven: Preheat the oven to 200°C (fan-assisted).
Prepare Potatoes: Wash the new potatoes and cut them into quarters if small, or halves if larger. Season with olive oil, salt, and pepper, and bake for about 20 minutes.
Make Breadcrumb Mixture: In a bowl, combine breadcrumbs with chopped sun-dried tomatoes, anchovies, capers, and garlic. Add lemon zest, salt, and pepper, and mix until homogeneous.
Prepare Sole Fillets: Lay the sole fillets on a work surface, spread the aromatic breadcrumb mixture on each fillet, and roll them up.
Bake Sole: Place the sole rolls on the baking tray with the potatoes and drizzle with olive oil. Bake for another 10 minutes until the fish is cooked and flakes easily.
Make Green Sauce: In a mixer, combine parsley, garlic, olive oil, lemon juice, salt, and pepper. Blend until smooth, adding water if necessary to adjust consistency.
Toast Remaining Breadcrumbs: Toast any leftover aromatic breadcrumbs in a pan until crispy.
Serve: Once cooked, serve the sole rolls hot on a plate with new potatoes, garnished with green sauce, toasted breadcrumbs, and fresh marjoram.