Directions. 1  1The main secret here is not to slice the zucchini too thin. Thin zucchini cooks through too quickly and turns into mush. 2  2Brush all sides of the zucchini strips/slices with olive oil. 3  3Sprinkle all sides with the Kosher salt, black pepper and minced rosemary.  4Preheat the grill to medium-high heat. 5Once the grill is ready, place the zucchini on the grill and grill directly, with the lid open for 3 minutes (turning halfway if you want some pretty grill marks). 6Flip the zucchini over and continue to grill for another 3 minutes on the other side.