Preheat a stovetop or outdoor grill over high heat. Rub the corn with the oil and place on the hot grill. Cook, turning often, until the corn is charred all around, about 8 minutes total. Remove from the heat and let cool slightly before cutting the kernels off the cob.
Place a large skillet over medium-high heat with the butter. Once melted, stir in the shallot, garlic and half of the corn. Cook until softened, about 5 minutes. Season with salt, pepper and cayenne.
Add the cream cheese and heavy cream and cook over low heat until the mixture has reduced by half, and slightly thickened.
In the meantime, bring a large pot of cold water to a boil. Season liberally with salt, and add the gnocchi. Cook according to package directions. Remove about 1/2 cup of the pasta cooking water before draining the gnocchi and add it to the sauce.
Stir the cooked pasta to the sauce and stir in the cotija cheese, and lime juice. Give it a taste and adjust seasoning accordingly, adding more salt or pepper as needed. Garnish with the remaining corn, cilantro and paprika.