Crispy Eggplant and Portobello Mushroom and Cheese Sandwiches

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Vegetable oil cooking spray

1/2 cup all-purpose flour 

1/2 teaspoon kosher salt 

1/4 teaspoon freshly ground black pepper 

3 large eggs, beaten, at room temperature 

2 cups panko breadcrumbs 

Four 1/2-inch-thick eggplant slices (1/2 a medium eggplant) 

Four 4-inch diameter portobello mushrooms, stemmed 

2 tablespoons extra-virgin olive oil, for drizzling, optional 

Four 1/2- to 3/4-inch-thick slices country wheat bread, toasted or grilled 

3/4 cup jarred tomato-basil sauce, such as Giada De Laurentiis for Target 

8 ounces gruyere cheese, shredded 

2 cups arugula