Blend Creamy Walnut Milk Base: In a high-speed blender, combine 1 cup of chopped walnuts with 1 cup of whole milk. Blend on high until the mixture is completely smooth and creamy. Strain the walnut milk through a nut milk bag or double-layered cheesecloth into a bowl, gently stirring to help it pass through. Discard solids or reserve for another use.
Create Banana Walnut Purée: Return the strained walnut milk to the blender. Add peeled bananas and blend until the mixture is smooth and fully combined. Set aside.
Thicken the Milk Custard: In a small bowl, whisk cornstarch with ¼ cup of milk until smooth—this will be your thickener. In a medium saucepan over medium-high heat, warm the remaining ¾ cup milk along with honey (or sugar), stirring occasionally. Once it begins to steam and small bubbles form at the edges, reduce the heat and slowly whisk in the cornstarch slurry. Continue cooking, stirring constantly, until the mixture thickens slightly and coats the back of a spoon.
Cool the Custard Base Quickly: Remove the saucepan from heat. Prepare an ice bath by placing the saucepan in a large bowl filled with ice and cold water. Stir occasionally until the custard cools to room temperature.
Combine Creamy Elements: To the cooled custard, stir in the salt, vanilla extract, reserved banana-walnut purée, and heavy cream. Whisk until well incorporated. Cover the mixture and refrigerate for at least 4 hours or overnight for optimal flavor and texture.
Churn and Add Mix-Ins: Pour the chilled mixture into your ice cream maker and churn according to your machine’s instructions. Just as the ice cream reaches a soft-serve consistency, fold in the remaining ½ cup chopped walnuts and chopped semi-sweet chocolate.
Optional Chocolate Swirl Finish: In a small bowl, microwave chocolate with heavy cream and oil in 20-second bursts, stirring in between until melted and smooth. Stir in instant coffee powder if using. Drizzle or swirl this into the churned ice cream as you transfer it to a storage container.
Freeze to Set: Spoon the ice cream into a freezer-safe container. Press a piece of parchment paper directly over the surface to minimize ice crystals. Seal with a lid and freeze for at least 3 hours or until firm.