Position an oven rack in the center of the oven, and preheat to 350 degrees F. Butter a 9-inch round cake pan.
For the topping: Melt the butter, brown sugar and lemon juice together in a microwave-safe small bowl in the microwave. Spread the mixture over the bottom of the prepared pan. Cover it with the starfruit slices by nestling them next to one another and overlapping (it will look crowded). Set aside.
For the cake: Spread the pecans out on a baking sheet, and bake until nicely toasted, 8 to 10 minutes. Let cool, then pulse in a food processor until finely ground. Whisk together the ground pecans, flour, cinnamon, baking powder, baking soda, nutmeg, salt and allspice. Set aside.
Beat the butter and brown sugar with an electric mixer on medium-high speed until light and fluffy, about 5 minutes. Add the eggs one at a time, beating to incorporate after each addition. Scrape down the side of the bowl as needed. Adjust the mixer speed to low, and add half the flour mixture, then the yogurt, then the remaining flour.
Pour the batter into the pan, spread it out into an even layer and give it a few taps on the counter. Bake until golden brown, a toothpick or cake tester comes out clean in the center and the cake pulls away from the edges, 45 to 50 minutes. Let cool on a wire rack until the pan is cool enough to handle, then run a knife along the edge and invert the cake onto a serving platter. Let cool completely before serving.
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