Cut each zucchini lengthwise into quarters. Thinly slice quarters.
Melt butter with vegetable oil in a large skillet over medium-high heat; add zucchini and garlic, and sauté 3 to 4 minutes.
Add corn and next 3 ingredients; cook, stirring often, 2 to 3 minutes or until zucchini is tender. Sprinkle with cheese and basil; heat until cheese melts.
* 2 cups fresh corn kernels (about 4 ears) may be substituted.