Bring grill up to medium heat. Lightly oil the grill grates with a grill brush to keep zucchini from sticking.
Spray zucchini slices with cooking spray on each side (or rub with oil if preferred). Sprinkle lightly with salt and pepper.
While grill is coming to temperature, start preparing glaze by heating vinegar and sugar in a small pan over medium heat, whisking to dissolve sugar. Bring to a simmer, then reduce heat to low.
Let simmer, stirring occasionally until vinegar has reduced by about half and sauce coats a spoon (about 10 minutes). It will continue to thicken as it cools so don't over do it!
Remove glaze from stovetop and let cool for 2-3 minutes while finishing zucchini (no more than 5 minutes or sauce may get too thick).**
While sauce is reducing, lay zucchini slices out flat on the grill and cook with grill covered for about 3-5 minutes. Flip and cook for about 3-4 minutes on the other side (exact cooking time will depend on temperature of grill, placement, and thickness of zucchini).
Remove zucchini from grill and spread out, slightly overlapping on a serving plate. Drizzle glaze over zucchini and then sprinkle with chopped basil and feta. Serve immediately.
*To make this recipe even easier, you can skip making the glaze yourself and you a store bought glaze instead. I get this one from Trader Joe's. **If sauce becomes too thick to pour, rewarm adding a small amount of water to thin it out.