Heat 1 tablespoon oil in a large skillet or wok over medium-high heat. Add cubed tofu and cook, turning occasionally, until golden and crisp on all sides, about 6-8 minutes. Transfer to a plate.
In the same pan, reduce heat to medium. Add the remaining 1 tablespoon oil and the green curry paste. Stir-fry for 1-2 minutes until deeply fragrant and slightly darkened.
Scoop the thick coconut cream from the top of the can (about 3-4 tablespoons) into the pan. Stir and cook for 2 minutes until it releases a glossy sheen. Pour in the remaining coconut milk and ½ cup water. Add kaffir lime leaves if using. Bring to a gentle simmer.
Add broccoli, bell pepper, and bamboo shoots. Simmer for 4-5 minutes until vegetables are crisp-tender.
Return the tofu to the pan. Stir in sugar, tamari, and lime juice. Simmer for 2 minutes, then remove from heat. Fold in Thai basil leaves, reserving a few for garnish. Taste and adjust seasoning.
Divide steamed jasmine rice among bowls. Ladle the curry over the rice, garnish with extra basil leaves and a lime wedge. Serve immediately.