Kumbakonam Degree Coffee is a regional speciality with its own near-mythic status: a strong filter coffee made with freshly ground beans (a blend usually around 80% coffee and 20% chicory), full-fat cow's milk, and a generous spoonful of sugar, served frothed back and forth between a metal tumbler and a wider dabarah to cool it to drinking temperature.
There is no single place to drink it — every old-style tiffin restaurant in town will serve a version, and locals will argue passionately about whose is best. Sri Mangalambika Vilas, Sri Krishna Bhavan, and the various branches of Mami Mess are all reliably good. Order it 'degree' and 'less sugar' if you prefer less sweetness. A morning round of one good filter coffee per shop is one of the better ways to walk through the old town.