Preheat oven to 400 degrees. Grease a square, or medium-sized, baking dish with the olive oil and set aside. In a large pot of salted water, boil the rotini as instructed on the package, around 8 minutes for al dente.
While the noodles are cooking, in a large bowl add the heavy cream, ricotta, asiago, marinara, garlic, basil, salt and pepper. Stir gently to combine until smooth.
Drain the noodles, then add the sauce mixture and stir until thoroughly coated. Add to the greased baking dish, then sprinkle with the breadcrumbs and drizzle with the melted butter. Bake uncovered for 20 minutes, or until the breadcrumbs are golden brown. Serve immediately.