In a tall blender (would not recommend using an immersion or a single serving blender here), blend the ube ice cream, ice and coconut milk until homogenous. If it's too watery, I'd recommend adding more crushed ice and blending again, or freezing the milkshake until the milkshake along the sides of the blender canister get a little icy and slushy.
In three tall glasses, smear 1 T ube jam in each along the walls of the cup (using a spoon is easiest). Divide the milkshake between the cups and enjoy!
Recipe Notes
If you can't find ube ice cream, you can use vanilla ice cream instead and add some of the jam to the milkshake itself. I'd start with ¼ cup, and add more until you reach your desired flavor and color (though it likely won't be as purple as the milkshake pictured here).