In a medium saucepan, whisk together the coconut milk, granulated sugar, and corn syrup.

Heat over medium-low heat for 5-7 minutes, whisking constantly until the sugar is fully dissolved. Do not allow to boil.

Remove from heat and whisk in the butterfly pea flower powder, vanilla extract, and sea salt until the color is vibrant and uniform.

Transfer the liquid base to a bowl and refrigerate for at least 4 hours, or until thoroughly chilled.

Pour the chilled mixture into an ice cream maker and churn according to the manufacturer's instructions, typically 20 to 25 minutes.

During the last 2 minutes of churning, gradually add the chopped vegan chocolate chip cookies and sandwich cookies until distributed.

Transfer the ice cream to a freezer-safe container and freeze for an additional 4 hours to achieve a scoopable consistency.