Plump the tempeh: Place the tempeh in a saucepan with enough water to just cover the block of tempeh by ¼-inch of so. Season the water with tamari soy sauce. Bring to a boil, reduce the heat, and cook about 5 minutes, turning the tempeh once during this time.
Remove the tempeh from the water. Drain and cut into 1/2-inch cubes. Set aside.
Over medium flame, heat the oil in a large skillet. Add the onion and cook about 5 minutes, stirring occasionally, until the onion is translucent.
Stir in the cubed carrot and potato, along with the smoked paprika and salt. Season generously with pepper. Make sure everything is mixed together, then put a lid on top and lower the heat. Cook until the potatoes are almost tender to the bite, about 10 minutes. They will finish cooking while the kale cooks.
Stir in the chopped kale, cover again, and cook until the kale is soft and easy to bite. When the vegetables are done, stir in the tempeh. Heat until the tempeh is hot.
At this point, the hash is ready to serve.
If adding eggs, reduce the heat to low. Make 4 holes in the hash, pushing the vegetables out of the way. Break an egg into each gap. (See notes)
Sprinkle salt and pepper over the eggs, cover, and cook about 10 minutes, until the eggs are just set. Serve immediately. If you wish, serve with salsa.