Step 1

If using a gas grill, preheat to medium-high (about 375 degrees). If using a charcoal grill, light the charcoal or wood briquettes; when they are ready, distribute them evenly under the cooking area for direct heat. For a medium-hot fire, you should be able to hold your hand about 6 inches above the coals for about 4 to 5 seconds.

Step 2

Grill the poblanos until they are blistered and completely charred on the outside, 6 to 8 minutes, turning them frequently with tongs. Transfer them to a bowl and cover with a plate. Let them steam for at least 10 minutes and up to 2 hours. Fill the bowl with water and use your fingers to remove the charred skin, then split open each pepper and discard the stem, cluster of seeds and veins. Pat the peppers dry and tear into strips. (If desired, you can char the poblanos under an oven broiler instead.)

Step 3

Cut each zucchini and eggplant in half crosswise, then cut them lengthwise into 1/4-inch slices. Brush the zucchini and eggplant slices with the olive oil. Sprinkle with ½ teaspoon of the salt and the pepper. Grill the zucchini and eggplant slices on one side until lightly charred and fork-tender, 6 to 8 minutes. Allow to cool slightly. (If desired, you can cook the eggplant and zucchini until lightly charred on one side under the broiler instead.)

Step 4

In a blender, combine the cilantro, canola or safflower oil, vinegar, garlic, brown sugar (if using) and the remaining 1 teaspoon salt and puree until smooth. Taste and add more salt, if needed. Pour the vinaigrette into a large bowl. Add the eggplant and zucchini and the poblano strips and gently toss. Let the vegetables sit for at least 5 minutes and up to 30 minutes before assembling the sandwiches.

Step 5

Split the rolls in half and toast them lightly. Place a generous amount of the dressed vegetables on the bottom halves and top each with 1/4 cup of cheese. Put the top halves of the rolls on top, press together, and serve. (If you’d like, you can split the rolls on the top, leave them hinged and stuff the vegetables inside, hot-dog-style.)