Preheat grill or grill pan over medium-high. In a small bowl, stir together 1 tablespoon oil with cumin and garlic; season with salt and pepper. Rub tomatoes with flavored oil.
Brush both sides of tortillas with 1 tablespoon oil; season with salt and pepper. Grill one side of tortilla until puffed and golden, about 2 minutes. Flip tortillas and divide cheese among them. Cook until cheese has melted, 2 minutes; transfer to a platter. Add tomatoes to grill and cook until charred and slightly softened, about 4 minutes.
Toss beans with cilantro, lime juice and remaining 1 teaspoon oil. Top tostadas with arugula, grilled tomatoes and dressed beans. Serve avocado on the side. Sprinkle with additional salt and pepper and serve with lime wedges.
Before her diagnosis, Caroline wrote a book on cakes called Cake Magic!. She started developing a birthday cake using her gluten-free mix found in that book. Check out other recipes she’s developing for her new life—and the stories behind them—on her blog, The Wright Recipes. Her next book, Catalan Food, written with chef Daniel Olivella, comes out in early September from Clarkson Potter.