Warm the oil over medium heat in a deep 12-inch lidded frying pan or medium-sized pot.
Add the onion, celery, garlic, ginger, and salt. Sauté for a few minutes, stirring frequently, until onion and celery are beginning to soften and turn translucent.
In a small bowl or glass measuring cup, whisk together the coconut milk, curry paste, soy sauce, fish sauce, and brown sugar.
Add the tomato paste to the pan and cook, stirring constantly, for one minute.
Pour the sauce mixture into the pan.
Add zucchini, potatoes, carrot, and tomato.
Bring to a boil, then cover, reduce heat, and simmer until potatoes are tender, probably about 20 minutes.
Turn off the heat and stir in the cilantro, and lime juice.