Heat a large skillet over high heat (brush or spray the bottom with oil if necessary). Add the corn kernels and cook for several minutes until they take on some color and begin to sputter and pop.
Stir in a tablespoon of butter, then sprinkle the flour over the corn and cook briefly before adding the milk or half and half.
Lower the heat and allow the milk to reduce, stirring occasionally. Season with salt and pepper. Stir in the basil then remove the corn to a bowl while you cook the potatoes.
Add enough oil to cover the bottom of the same skillet and turn the heat up to medium high.
Add the potatoes and leave them alone for a few minutes to brown. Continue to cook, stirring once in a while, until the potatoes are warmed through and golden colored on all sides.
Return the corn to the skillet and stir gently to combine. Add small amounts of butter or milk as desired to create the amount of sauce you like. Season again before serving.