In a small bowl, blend the butter with the bell pepper, basil, jalapeño and a generous pinch each of salt and pepper. Wrap the butter in plastic, forming it into a 4-inch log and refrigerate until firm, about 3 hours or for up to 3 days.
Light a grill. Lightly brush the corn with oil and grill over moderately high heat, turning, until tender and charred all over, 10 to 12 minutes. Slice the butter into pats and serve with the corn.