Heat broiler. On rimmed baking sheet, brush both sides of eggplant or mushrooms with oil and season with ¼ teaspoon each salt and pepper. Broil until tender and browned in spots, 4 to 7 minutes.
Meanwhile, in medium bowl, mash avocados with lemon juice, red pepper flakes, and ½ teaspoon each salt and pepper. Spread 4 slices toast with mashed avocados and remaining 4 slices with hummus, then add remaining fillings to make sandwiches, sprinkling flaky salt on tomato.
