Heat oil in a 10-inch nonstick skillet over medium heat.
Add zucchini, pepper, and onion; cook, stirring frequently, for 2 minutes, or until zucchini is tender.
Add basil and salt. Increase heat to medium-high; cook, stirring frequently, for about 30 to 60 seconds, or until the moisture has evaporated.
Add eggs and goat cheese to vegetable mixture. Stir until combined; cook, over medium heat, without stirring, for about 2 to 3 minutes, or until the bottom is light golden. As it cooks, lift the edges and tilt the pan so uncooked egg will flow to the edges.
Reduce heat to low; continue cooking, covered, for 15 to 18 minutes, or until knife inserted in center comes out clean.