Make your own labneh by straining the yogurt into a cheesecloth-lined mesh strainer set over a deep bowl for 4 hours in the refrigerator, but not longer. The labneh can be made up to 2 days in advance.
To make the pistachio-sesame brittle, line a baking sheet with a silicone baking mat or grease it lightly with vegetable oil. Mix the pistachio and sesame seeds in a small bowl.
Spread the sugar in a medium, heavy-bottomed skillet and cook over medium heat, watching it carefully. When it begins to liquefy and darken at the edges, use a heatproof spatula to stir it very gently, encouraging the liquefied sugar around the edges to moisten and melt the sugar crystals in the center.
Tilt the pan and stir gently until all the sugar is melted and the caramel begins to smoke. Once it has a deep golden color, remove it from the heat and immediately stir in the nuts and seeds. Scrape the mixture onto the prepared baking sheet and spread it with a spatula into an even layer. Let cool completely. Once cooled, chop the brittle into bite-sized pieces with a chef's knife. Store in an airtight container until ready to use.
To make the ice cream, whisk together the labneh, cream, honey, sugar, and salt. Chill the mixture thoroughly in the refrigerator.
Freeze the labneh mixture in your ice cream maker according to the manufacturer's instructions. Serve with the brittle crumbled on top.