Heat 1/4 cup of the oil in a large nonstick saute pan. When it is hot, add 1/2 of the eggplant and 3/4 teaspoon of the salt. Cook until the eggplant is nicely browned and softened, stirring as necessary to promote even browning, about 5 minutes. Add half of the green onion bottoms, 1 tablespoon garlic, 1/4 teaspoon black pepper, 1/4 teaspoon crushed red pepper, 1/2 tablespoon sesame seeds, and 1/2 tablespoon of the sesame oil. Toss to combine. Transfer to a plate and set aside.
Repeat with the remaining ingredients plus the tofu.
Combine both batches in the same pan, add the green onion tops, and heat briefly until warmed through, 1 minute. Serve immediately.