In a saute' pan, heat oil over medium high heat. Add the aromatics- ginger, garlic, onion, turmeric; cook, stirring constantly, until fragrant for 5 minutes.
Add the heirloom tomatoes; cook, stirring often, until soft and juicy, about 5 minutes.
Pour in the liquids - coconut milk, water and fish sauce and also, at the same time, add the chicken and a pinch of salt. Bring to a boil then reduce to medium low and cook for 5 minutes.
Add the carrots and baby potatoes; cook, until fork tender, about 10 minutes. Taste. Add more salt if needed. Remove from heat.
Add the basil and squeeze the lime juice all over. Stir to combine. Divide among bowls. Serve with rice.