Grilled Summer Vegetable Bibimbap

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1/2 cup vegetable oil, plus more for the grill grates

3 tablespoons gochujang 

3 tablespoons soy sauce 

3 tablespoons rice wine vinegar 

2 tablespoons toasted sesame oil  

2 tablespoons toasted sesame seeds, plus more for serving  

1 tablespoon honey 

3 garlic cloves, finely grated 

1 medium Kirby cucumber, halved and thinly sliced 

1/2 teaspoon sugar 

Kosher salt 

1 pound large mushrooms, such as cremini, portobello or shiitake (stems removed if using shiitake)  

3 large red bell peppers, quartered  

1/2 medium head green cabbage, cored and halved 

1 large zucchini, cut on the bias into 1/2-inch slices 

6 scallions, root ends trimmed 

4 large eggs

6 cups cooked white rice (from 3 cups uncooked)