Make the caramel: Preheat the oven to 350º and grease a 9-inch cake pan. In a medium saucepan, cook the sugar over medium-high heat, stirring as needed, until an amber caramel has formed, 2 to 3 minutes. Add the softened butter and cook, stirring constantly until emulsified, 1 to 2 minutes. Immediately pour into the prepared cake pan, spreading to cover the entire bottom of the pan. Arrange the jackfruit, cut-side up, over the caramel.
Make the cake batter: In a small bowl, whisk together the flour, baking powder and salt. In a medium bowl, whisk together the light brown sugar, butter, vanilla, eggs and yolks. Fold the dry ingredients into the wet until a smooth batter is formed. Pour the batter over the jackfruit in an even layer and smooth the top with a rubber spatula.
Bake until the top of the cake is golden brown and a toothpick comes out clean when inserted into the center, 35 to 40 minutes. Remove the cake from the oven and let it slightly cool on a wire wrack, 5 to 10 minutes. Then invert the cake onto a plate.
Meanwhile, make the toffee sauce: In a medium saucepan, bring the half-and-half, light brown sugar and butter to a boil over medium-high heat. Cook, stirring constantly, until the sugar dissolves and the mixture has slightly thickened, 4 minutes. Stir in the lime juice, vanilla and salt, and cook for 2 minutes more. Transfer to a bowl and let cool completely.
To serve: slice the cake and divide between plates. Drizzle with the toffee sauce and serve with a scoop of butter pecan ice cream.