We prefer the texture and flavor of fresh tortellini (found in the refrigerated section of most supermarkets), but you can substitute frozen, if desired.
Bring 4 quarts water to boil in large pot. Add pasta and 1 tablespoon salt and cook, stirring often, until al dente. Reserve ½ cup cooking water, then drain pasta and return it to pot.
Melt butter in 12-inch skillet over medium heat. Add corn, shallot, Fresno chile, pepper, and ½ teaspoon salt and cook until vegetables are tender, 4 to 6 minutes. Transfer to pot with pasta.
Bring cream to simmer in now-empty skillet over medium-high heat. Reduce heat to medium-low and simmer, stirring often, until reduced to ¾ cup, 3 to 5 minutes. Off heat, stir in basil. Transfer to blender and blend with Parmesan and remaining ¼ teaspoon salt until smooth, about 1 minute. Add sauce to pot with pasta and toss to combine. Adjust consistency with reserved cooking water as needed. Season with salt and pepper to taste. Serve, topping portions with extra Parmesan and basil.
