Wrap tofu in several layers of paper towels. Place in a colander in the sink. Set a plate on top of tofu and weigh down with a large, heavy can. Let stand for at least 20 minutes.

Meanwhile, shake cans of coconut milk well prior to opening. Pour 1/2 of 1 can into a large saucepan. Bring to a simmer over medium heat. Whisk in curry paste until well blended. Add eggplant, onion, and bell pepper, stirring well with a rubber spatula to prevent breaking of tender eggplant during cooking.

Stir remaining 1 1/2 cans coconut milk, dark brown sugar, tamari, rice vinegar, and salt into the saucepan. Mix well. Increase heat and bring to a boil. Reduce heat to low and simmer until thickened, about 20 minutes.

Unwrap tofu and cut into bite-sized cubes. Stir into curry mixture. Cook until heated through, about 5 minutes. Add peas and cook until warm, 1 to 2 minutes more.