Heat 1 tablespoon of the oil in a medium saucepan over medium-high heat.
Add the onions and saute, stirring, until soft, about 4 minutes.
Add the lentils, chicken broth, soy sauce, 1/2 teaspoon salt and a few grinds of black pepper.
Bring to a simmer, add the kale and cook until the kale is tender and the stew is slightly thickened, about 15 minutes.
Remove from the heat, cover and keep warm.
Heat the remaining 1 tablespoon oil in a large nonstick skillet.
Once the oil is hot, crack the eggs into the skillet and cook until the whites begin to set up, about 2 minutes.
Sprinkle each egg with pepper, cover and continue to cook until the white are completely set and the yolks are still runny, about 2 minutes more. Remove from the heat.
Divide the stew among four bowls, top each with an egg and serve with hot sauce.