DO-AHEAD TIP: Prepare brown rice.
Season eggplant and mushrooms with salt and pepper.
Heat 1 1/2 tablespoons of oil in a large skillet over medium-high heat; add eggplant and mushrooms; cook until vegetables are just becoming tender, 5 to 7 minutes.
Reduce skillet heat to medium and add remaining oil, onion, bell pepper, garlic, paprika, oregano, basil and crushed red pepper flakes; cook until onion is translucent.
Add cherry tomatoes, tomato sauce and tomato paste; cook for 2 to 3 minutes. Stir in rice and heat through. Remove from heat and serve.