Preheat the oven to 400°F (200°C).
In a mixing bowl combine 2/3 cup ricotta, 1/3 cup Parmesan, 2 teaspoons basil pesto, a pinch each of salt and pepper, and 2 tablespoons chopped fresh basil; stir until well mixed.
Spoon about 2 tablespoons of the ricotta filling onto each lasagna sheet and spread evenly, leaving a small border; then roll each sheet into a tight tube.
Spoon about 3/4 cup marinara sauce into the bottom of each oven-safe mug or dish, then sprinkle a layer of shredded mozzarella over the sauce.
Place three rolled lasagna sheets upright in each mug or dish on top of the mozzarella, pressing down gently so they stand together.
Top the rolls with about 1/2 cup additional marinara (or to taste) and a little Alfredo if desired; cover each mug or dish with foil.
Bake covered for 15–20 minutes, then remove the foil and bake a few minutes more if you want the cheese on top more melted and bubbly.
Carefully remove the mugs from the oven and invert each onto a plate by placing the plate over the mug and flipping it quickly so the rolls lift out with sauce on top.
Sprinkle with the remaining 2 tablespoons freshly grated Parmesan and additional chopped basil before serving.