In a small blender jar, add the chopped cucumber, grated/chopped coconut, ginger, green chilli, cumin seeds, black peppercorns, coriander leaves, and a splash of water. Grind this into a very smooth, fine paste.
In a medium bowl, combine the whisked curd or buttermilk, cucumber paste, and salt. If the mixture is too thick, you can thin it out with a little water or buttermilk; Thambuli is typically thinner than a standard raita.
Heat oil in a small pan. Once hot, add the mustard seeds and let them splutter.
Add the cumin seeds, red chili, and curry leaves. Once the leaves are crisp and the aroma fills the kitchen, pour this hot tempering directly over the cucumber tambuli.
Mix nicely and Cucumber Tambuli is ready to serve.