Preheat oven to 375°F. Line a baking sheet with a silicone mat. Cut paneer into 1-inch cubes and place in a bowl. Add 2 tablespoons oil, turmeric, salt, and breadcrumbs. Toss so that all sides of the cheese cubes are coated. Spread the cheese onto the prepared baking sheet and cook, turning once, until each cube of cheese is golden brown on 2 sides, about 20 minutes.

While the cheese cooks, tear the leaves of the chard from their ribs into bite-sized pieces. Slice the ribs very thinly like you would stalks of celery. In a large skillet over medium heat, warm 3 tablespoons oil. Add onions and sliced chard ribs. Cook, stirring often, until the vegetables have softened, about 10 minutes. Add ginger, chile, and curry and cumin powders. Stir to coat the vegetables with the spices. Add chard leaves and coconut milk. Bring to a simmer and cook until the leaves are wilted, about 5 minutes. Stir in tomatoes and reduce heat to low. Remove paneer from the oven. Add to the skillet with the sauce and stir to combine. Serve hot over basmati rice.