Cut tofu into thirds lengthwise and eighths crosswise. Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add tofu and sprinkle with 1/4 teaspoon salt. Cook, stirring gently every 2 to 3 minutes, until browned on all sides, 6 to 8 minutes. Transfer to a plate.
Add the remaining 2 teaspoons oil to the pan and reduce heat to medium. Add onion, garlic, ginger and mustard seeds and cook until the onion is translucent, 4 to 6 minutes. Add spinach in batches small enough to fit in the pan and cook, stirring frequently, until all the spinach has been added and has wilted, 4 to 6 minutes more.
Meanwhile, combine yogurt, curry powder, cumin and the remaining 1/2 teaspoon salt in a small bowl. Add to the pan along with the tofu and cook until heated through, about 2 minutes.