Cut tofu into eight 1/2-inch-thick slices. Arrange on paper towels; drain 10 minutes. Spread both sides of each slice with mustard.
Heat 2 tablespoons oil in large nonstick skillet over medium-high heat. Add onion and ginger; sauté 1 minute. Add kale, sweet potato, and lime juice. Cover, reduce heat to low, and cook until potato is tender and kale is wilted, about 12 minutes.
Meanwhile, heat remaining 2 tablespoons oil in another large nonstick skillet over medium heat. Add tofu; cover and cook until heated through and crisp, about 2 minutes per side (some mustard seeds may fall off tofu).
Arrange kale and sweet potato mixture on plate. Overlap tofu slices atop vegetables and serve.