Preheat the oven to 350° and line a baking sheet with parchment paper. In a food processor, pulse the flour with the light brown sugar and salt. Add the butter and tahini and pulse until moist crumbs form. Add the black sesame seeds and pulse to combine. Scatter the tahini crumbs on the baking sheet and bake them for about 20 minutes, until they are golden and crisp. Let cool, then break up any big clumps.
Meanwhile, in a large skillet, combine the plums and peaches with the granulated sugar and lemon juice and cook over moderate heat, stirring occasionally, until the fruit is just softened and the juices are thickened, about 10 minutes.
Scrape the fruit into a shallow gratin dish or glass pie plate and sprinkle with the crumbs. Bake in the center of the oven until the fruit is bubbling, about 10 minutes. Let cool for 5 minutes, then serve.