Brush vegetables with olive oil and place on a medium to medium-hot grill (375 to 475 degrees), 4 to 6 inches from heat source. For easy turning, use a hinged grilling basket or grill grid. Serve some of the vegetables hot off the grill or at room temperature for tonight's dinner.
Store the rest: Cut vegetables into bite-size pieces. Put each type in a separate ziptop food bag. Add a little olive oil to each bag to lightly coat vegetables. Press air out of bags, seal and refrigerate up to 5 days. You'll have about 6 cups total, depending on how much was used the first night.