Combine blackberries, 3 tablespoons honey, lemon juice, 1 teaspoon vanilla extract, and water in the saucepan.

Cook over medium heat, stirring occasionally, until the berries break down and the mixture becomes thick and jammy, about 20 minutes.

Transfer the blackberry compote to the metal bowl and cool it completely in the freezer, about 20 minutes.

Stir 1/2 cup pistachios, almond flour, 3 tablespoons honey, almond extract, and 1 pinch salt in a mixing bowl until a cookie-dough-like mixture forms.

Spread the crumble mixture evenly on the parchment-lined baking sheet.

Bake at 325°F (165°C) until the edges begin to brown, about 12 to 16 minutes.

Cool the baked crumble completely in the freezer, then break it into small pieces.

Blend heavy cream, ricotta, remaining 1 cup pistachios, remaining 7 tablespoons honey, remaining 1/2 tablespoon vanilla extract, and remaining pinch salt until smooth.

Pour the blended base into the Instant Pot InstantChill and select the ice cream setting for 16 minutes.

Add the cooled blackberry compote and half of the crumble when the appliance signals for mix-ins.

Serve the ice cream immediately and top each portion with the remaining crumble.