Place the tofu between layers of paper towels and weigh them down with a heavy skillet to remove excess water. Set aside to drain for 10 minutes.
Combine the curry paste, sugar, and fish sauce; put half this sauce in a resealable plastic bag. Add the tofu, seal, and set aside for 15 minutes.
In a saucepan, combine the green beans, broth, oil, and the remaining curry. Simmer until the beans are tender, about 5 minutes. Cover to keep warm.
Lightly coat a nonstick skillet with vegetable cooking spray and place it over medium heat. When hot, add the tofu and cook until golden, about 4 minutes per side. Transfer to a dinner plate and cover.