Preheat the oven to 350 degrees F (175 degrees C). In a mixing bowl, combine the breadcrumbs, panko, gruyere cheese, and garlic, and stir well to incorporate the ingredients.
In a separate bowl, whisk together the soy sauce, balsamic vinegar, and 1 teaspoon of olive oil until thoroughly combined.
Slice the tomatoes into 1/4 to 1/2-inch-thick rounds.
Brush the soy sauce mixture generously over both sides of each tomato slice. Sprinkle salt and pepper to taste, then dip the slices into the breadcrumb mixture, coating both sides evenly.
Lightly grease a baking sheet with cooking spray or oil, and arrange the tomato slices in a single layer. Drizzle 1 tablespoon of olive oil evenly over the top of the tomatoes.
Bake the tomatoes in the preheated oven for 15 to 20 minutes, until they are tender and the breadcrumb coating is golden brown. Turn on the broiler for the last few minutes to lightly brown the tops. Remove from the oven and serve immediately.