Step 1

Heat grill or grill pan to medium-high heat.

Step 2

Trim the stems from the mushrooms. Slice the eggplant, squash, and zucchini into 1/4-inch-thick rounds. Brush vegetables with canola oil, sprinkle with salt, and grill until softened and grill marks have formed — about 10 minutes each side. (Brush with oil as needed to prevent sticking.)

Step 3

Transfer to a baking pan. Heat broiler to low. Split the buns, brush the tops with the sesame oil, and sprinkle with sesame seeds. Layer the squash, zucchini, eggplant, and mushroom on the bottom bun halves. Top each with cheese and broil until cheese melts, about 1 minute. Top with remaining seeded bun tops and serve hot.