Preheat the oven to 375°F (180°C) and lightly oil a 6-cup muffin pan or spray with nonstick spray.
Bring a large pot of salted water to a boil. Blanch each lasagna sheet for 2–3 minutes until slightly softened but not falling apart, then transfer to a plate; repeat for all sheets.
Gently fit each softened lasagna sheet into a muffin cup, pressing to form a cup shape and avoiding tearing the pasta.
In a small bowl, combine the drained ricotta with chopped basil and season with salt and black pepper to taste.
Transfer the ricotta mixture to a piping bag or use a spoon and fill each lasagna cup with about 1 tablespoon of the ricotta filling.
Spoon 1–2 tablespoons of marinara sauce over the ricotta in each cup to cover the filling.
Top each cup with a small amount of the cubed mozzarella. Drizzle lightly with olive oil and season with a little black pepper.
Bake the lasagna cups for 10–12 minutes, until the cheese melts and the pasta edges are golden and crisp.
Remove from the oven and serve immediately, garnished with reserved basil leaves.