Step 1

1 If using a gas grill, preheat to medium-high (about 375 degrees)

Step 2

2 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

Step 3

3 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 4

4 Grill the poblanos until they are blistered and completely charred on the outside, 6 to 8 minutes, turning them frequently with tongs

Step 5

5 Transfer them to a bowl and cover with a plate

Step 6

6 Let them steam for at least 10 minutes and up to 2 hours

Step 7

7 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

Step 8

8 Pat the peppers dry and tear into strips

Step 9

9 (If desired, you can char the poblanos under an oven broiler instead

Step 10

10 )

Step 11

11 Cut each zucchini and eggplant in half crosswise, then cut them lengthwise into 1/4-inch slices

Step 12

12 Brush the zucchini and eggplant slices with the olive oil

Step 13

13 Sprinkle with ½ teaspoon of the salt and the pepper

Step 14

14 Grill the zucchini and eggplant slices on one side until lightly charred and fork-tender, 6 to 8 minutes

Step 15

15 Allow to cool slightly

Step 16

16 (If desired, you can cook the eggplant and zucchini until lightly charred on one side under the broiler instead

Step 17

17 )

Step 18

18 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

Step 19

19 Taste and add more salt, if needed

Step 20

20 Pour the vinaigrette into a large bowl

Step 21

21 Add the eggplant and zucchini and the poblano strips and gently toss

Step 22

22 Let the vegetables sit for at least 5 minutes and up to 30 minutes before assembling the sandwiches

Step 23

23 Split the rolls in half and toast them lightly

Step 24

24 Place a generous amount of the dressed vegetables on the bottom halves and top each with 1/4 cup of cheese

Step 25

25 Put the top halves of the rolls on top, press together, and serve

Step 26

26 (If you’d like, you can split the rolls on the top, leave them hinged and stuff the vegetables inside, hot-dog-style

Step 27

27 )