The best way to cut zucchini is to cut them lengthwise. I prefer the thick slices over thin slices because they're easier to handle on the grill and allow you to get great grill marks before they're overcooked. place them diagonally on the grill grates so you'll see the gorgeous grill marks when you cut them into half moons. You can also cut them into rounds so they're easier to handle on the grill then cut them into half moons after they cool.