Heat 1/4 cup oil in a large skillet over medium. Add eggplant, season generously with salt, cover, and cook, stirring occasionally, until tender, about 10 minutes. Transfer to a plate.

Add remaining 2 tablespoons oil to skillet over medium heat. Add garlic and red-pepper flakes and cook, stirring, until fragrant, 1 minute. Add tomatoes and simmer, stirring, until slightly thickened, 5 minutes. Return eggplant with any juices to skillet; season with salt. Add gnocchi in a single layer atop eggplant, cover, and cook until tender, 6 to 8 minutes (or, if using frozen, about 1 minute more). Sprinkle with basil and serve, topped with a spoonful of ricotta, more basil leaves, pepper, and a drizzle of olive oil.