Combine dry gin, bitters, coffee liqueur, and orange juice in a mixing glass and stir. Decant contents into a microwave-safe container and microwave for 30 seconds. Add ice to a blender and pour contents of container into it. Add clamato juice and brown sugar, cap container, and turn blender on. When mixture has the consistency of a frozen drink, pour into highball glass. Garnish with straw, a dash of kosher salt, and peppermint leaves.