Place rack in upper third of oven and heat broiler.

In large ovenproof skillet, heat 1 Tbsp olive oil over medium-high. Add panko to skillet and heat, stirring often, until golden brown and crisp, about 3 minutes. Remove panko from skillet and set aside.

In same skillet, heat 1 Tbsp olive oil over medium. Add eggplant and 1/4 tsp salt and heat, stirring occasionally, until softened and browned, about 10 minutes. Remove eggplant from skillet and set aside.

In same skillet, heat remaining 1 Tbsp oil over medium. Add onion and remaining 1/4 tsp salt; heat for 5 minutes, stirring occasionally. Add garlic and heat 2 minutes. Stir in thyme and red pepper flakes. Add tomatoes to pan and heat until sauce is slightly thickened, 5 to 7 minutes.

Place eggplant and beans in pan and stir into tomato sauce. Sprinkle panko on top and then sprinkle mozzarella and Parmesan over panko so it’s completely covered. Place pan in oven and broil until cheese is melted and blistered, about 3 minutes. Remove pan from oven and scatter on basil.