Scrape the thick, white layer of coconut milk fat off the top of the cans of coconut milk and transfer to a large saucepan, discard the opaque liquid. Add almond milk, dates, ½ cup mint leaves, honey, and salt to saucepan. Bring mixture to a simmer over medium-high heat and cook 5 minutes then remove from heat. Let steep 15 minutes then remove and discard mint. Transfer mixture to a blender with remaining ½ cup mint and blend until smooth (if using a standard blender, blend mixture in two batches).
Transfer all but 2 tablespoons of the blended mixture back to the saucepan. Bring mixture to a low simmer over medium-high heat, whisking constantly. Whisk the 2 tablespoons of reserved mixture with arrowroot starch, then whisk into simmering mixture and cook 30 seconds to 1 minute more until thickened. Remove from heat and whisk in matcha, if using. Transfer mixture to an airtight container and refrigerate until completely chilled, at least 4 hours or up to 3 days.
When ready, transfer mixture to the bowl of you ice cream maker and churn according to manufacturer's instructions, it should look like soft serve ice cream. Transfer ice cream to an airtight container and freeze until firm, about 2 hours.
When ready, scoop a scant ⅓ cup of ice cream onto bottom side of half of the cookies, then place remaining cookies, bottom side down, on top of ice cream and gently press to even out ice cream layer. Transfer to an airtight container and freeze until ready to serve.
Let ice cream sandwiches sit at room temperature 5 minutes before serving.