For the salsa verde: Place the parsley, mint, and chopped shallot on a cutting board. Sprinkle with ¼ teaspoon salt and chop together until minced. Transfer to a small bowl. Mix in the oil, lemon zest and juice. Season to taste with salt and a pepper.
For the Polenta: Combine the water, cornmeal, olive oil, salt, and a generous amount of pepper in a medium microwave-safe bowl. Mix to combine. Cook in the microwave at high setting for 5 minutes. Stir thoroughly, and then cook at high setting for 5 more minutes. Stir well. Mix in the cheese.
Meanwhile, cook the kale and eggs: Heat 1 tablespoon of oil in a large nonstick skillet over medium heat. Add the kale, sprinkle with salt and pepper and stir to coat with oil. Add ¼ cup water, cover and cook until the kale is tender, about 5 minutes. Add the kale to the polenta and stir to combine.
Quickly rinse out the skillet, dry well, and return to medium heat. Add the remaining 1 tablespoon oil and heat until hot. Add the eggs. Sprinkle with salt and pepper and let sizzle until the whites are set and the yolks are still runny.
Divide the polenta among 2 plates or shallow bowls. Top with the eggs. Grate a little Parmesan cheese on top and serve with the salsa verde, if using.