Combine the black raspberries, 1/4 cup sugar, and lemon juice in a saucepan over medium heat. Stir occasionally and cook for 8-12 minutes until the mixture thickens and the raspberries break down, releasing their deep purple juice. The lemon juice brightens the berries' flavor and prevents the compote from tasting one-dimensional. Once thickened, transfer to a bowl and let cool completely—this can happen at room temperature while you work on the next steps.
While the compote cools, preheat your oven to 350°F. In a bowl, combine the graham cracker crumbs, 1 tbsp sugar, melted butter, and salt, stirring until the mixture resembles wet sand. Press this mixture firmly into a 9x13 inch baking pan or similar size, creating an even base layer. Bake for 10-15 minutes until golden and fragrant, then remove and let cool completely. Once cooled, break the crust into bite-sized pieces—you want texture pieces, not a solid slab.
In a large mixing bowl, beat the softened cream cheese (it should be around 70°F for smoothness) for 2-3 minutes until completely smooth and lump-free. This is crucial—any lumps will persist through the final shake. Gradually add the 3/4 cup sugar while beating, then add the 1 cup milk, 2 cups cream, vanilla, and 1/4 tsp salt. Beat for another 1-2 minutes until well combined and slightly fluffy. I always use Nielsen-Massey Madagascar Bourbon vanilla here because the quality really shines through in a milkshake.
Stir half of the cooled raspberry compote from Step 1 into the ice cream base, folding gently to create swirls rather than a uniform color. Pour the mixture into an ice cream maker and churn according to manufacturer's instructions, typically 20-25 minutes, until it reaches a soft-serve consistency. Transfer the churned ice cream to a freezer-safe container, alternating layers with the graham cracker pieces from Step 2 and the remaining raspberry compote. Freeze for at least 2-3 hours until firm enough to scoop.
Scoop about 1.5 cups of the layered ice cream into a blender. Add 1/2 cup milk and 1.5 tbsp malt powder—the malt adds a nostalgic, nutty depth that complements the bright berries beautifully without overpowering them. Blend until smooth and pourable, about 30-45 seconds, stopping to scrape down the sides if needed. Pour into a chilled glass and top with extra graham cracker crumbs for texture and visual appeal.