Break or cut each corn cob in half. Heat vegetable oil in a large skillet over medium heat and pan-fry corn until golden brown on all sides, about 10 minutes, turning often. Remove corn.
Pulse onion, garlic, and ginger to a smooth paste in a food processor; mix in curry leaves, cumin seeds, chili powder, and sugar. Cook paste in the hot oil over medium-low heat until the oil begins to separate, stirring often, about 10 minutes.
Remove skillet from heat and let the paste cool; stir in the yogurt. Return corn to yogurt sauce and spoon sauce over corn to serve.