Heat a dutch oven or wok over medium-high heat and add the olive oil. After 90 seconds when the oil is hot, add the tofu in a single layer and cook until golden brown on all sides, turning occasionally. Transfer to a plate and set aside.
Trim off any dry external leaves from the lemongrass, cut it into 3 inch sections, and smash the lemongrass with the side of a heavy knife or cleaver so that when it cooks it releases its oils into the curry.
Reduce the heat to medium and add the coconut oil to the pan. After 90 seconds when the oil has melted, add the lime leaves and lemongrass. Stir in the yellow curry paste and turmeric and cook for 30 seconds, stirring continuously.
Pour water, carrots and potatoes, then bring to a simmer over medium heat. Cover and cook until the potatoes are just fork-tender.
Once the potatoes are soft, add the green beans, bamboo shoots, and bell pepper. Stir well and cook, uncovered, until the vegetables are tender but not lifeless.
Stir in the coconut milk, brown sugar, lime juice, and salt.
Return the fried tofu to the pan along with the Thai basil and cook for 2 more minutes, allowing it to absorb the flavors.
Serve hot with jasmine rice, garnished with cilantro and sliced Thai green chilies if desired.