An hour before grilling, soak the cedar planks. When ready to cook, heat the grill to 350 to 400 degrees F.
Evenly distribute the oil on the salmon and corn. Evenly distribute 3/4 teaspoons of salt and pepper (to taste) on top of the salmon.
Arrange the corn onto the grill. Place the planks onto the grill and then place the salmon onto the cedar planks. Grill for 14-20 minutes or until the salmon reaches 145 degrees F and the corn kernels are softened. Turn the corn one to two times while grilling. The corn and salmon may not finish at the same time. Cook accordingly.
While the salmon cooks, prepare the lemon-basil sauce. In a saucepan, melt the butter over low heat. Add the shallot and cook over medium heat for 3 to 4 minutes. Add the cream, basil, lemon zest and the remaining 1/4 teaspoon of salt. Stir to combine.
Reduce the heat and simmer for 10 minutes. Whisk in the parmesan and lemon juice. Continue to simmer for 5 minutes. Taste and adjust the seasonings with additional lemon juice, salt and pepper.
Top the grilled salmon and corn with the lemon-basil sauce and freshly chopped basil. Serve warm.