Blend non-dairy ice cream and non-dairy chocolate milk in blender until smooth. Set aside.
Combine 2 tbsp of chocolate coconut milk and chocolate chips in a bowl. Melt in microwave in short bursts (appx. 15 seconds), stirring between. Continue until melted and smooth.
Dip rim of glass in melted chocolate chips. Refrigerate 5 minutes to set slightly.
Crush vegan sandwich cookies into bite-sized pieces. Press pieces into chocolate on rim of glass until chocolate is covered.
Drizzle caramel and chocolate sauces inside glass. Pour milkshake into glass.
Top with non-dairy whipped topping.
Break or cut brownie and nut butter cups into bite-sized pieces and slide onto top 2-3 inches of each bamboo skewer. Place into milkshake.
Top with additional chocolate sauce and serve immediately.