Preheat the oven to 190C fan.
Brush one filo sheet with half of the butter, then sprinkle over one tablespoon of sugar. Lay the second filo sheet on top, press down, and brush with the remaining butter, sprinkle over the remaining sugar, the sesame seeds and salt. With the long side facing you, cut it in half vertically, then cut each rectangle into four triangles, for a total of 8. Arrange the triangles on a large, parchment lined baking tray and bake for about 6 minutes, until golden. Set aside to cool, then break roughly into large shards.
For the cherry compote, add all of the ingredients, except for the lime zest and juice, to a medium saucepan along with 4 teaspoons of water. Simmer on medium heat for about 10 minutes, stirring often, until the sauce has thickened and the cherries have broken down slightly. Remove from the heat and stir through the lime juice, then set aside to cool.
Whip the cream with the sugar until soft peaks form, then fold through the tahini.
To serve, arrange the cream, compote and brittle in alternating layers, to create a high stack. Finish with lime zest and more Aleppo chilli, if you like.