Heat 2 tablespoons oil in a large saucepan or wide pot over medium heat. Add curry paste and bloom in the oil, stirring frequently, until very fragrant, about 2 minutes. Stir in coconut milk and bring to a simmer. Add thawed meatballs and continue to simmer, stirring frequently, until meatballs are heated through, another 3 to 5 minutes. Season with salt and pepper to taste.
Heat the remaining tablespoon oil in another large pan over medium-high heat. Add the zoodles and a pinch of salt and cook, stirring occasionally, until zoodles are warmed through and some of their moisture has evaporated, about 5 minutes.
Evenly divide the zoodles among 4 bowls. Ladle curry over zoodles and top each with a few meatballs. Top each with sliced Thai bird chiles, basil, cilantro and black and white sesame seeds. Serve with lime wedges.