Preheat the oven to 400°F (200°C).
Make the filling: in a mixing bowl combine the ricotta, 1/3 cup Parmesan, 2 teaspoons basil pesto, a pinch of salt and pepper, and 2 tablespoons chopped fresh basil; mix until smooth.
Spoon about 2 tablespoons of the filling onto each lasagna sheet and spread it into a thin layer with the back of the spoon.
Roll each sheet tightly from one end to the other to form a tube; set rolls aside.
Prepare the rosa sauce: pour about 3/4 cup marinara into the bottom of an oven-safe mug or small deep dish, then add a layer of shredded mozzarella over the sauce.
Place three rolled lasagna sheets into the mug or dish on top of the mozzarella, pressing down gently to fit; repeat with a second mug or another dish for the remaining three rolls.
Spoon about 1/2 cup rosa sauce (mix marinara and Alfredo to taste if you want a pink/rosa sauce) over the rolls to cover, then sprinkle with remaining 2 tablespoons grated Parmesan.
Cover the mug or dish with foil and bake for 15–20 minutes, until cheese is melted and filling is heated through.
Remove foil and let cool 2 minutes, then invert each mug or dish onto a plate to release the rolls so sauce covers them.
Serve the roll ups sprinkled with extra shredded mozzarella or Parmesan and chopped fresh basil.