Heat 1 tablespoon oil in a medium skillet over medium-high burner. Cook garlic until barely golden, stirring frequently, about 1 minute. Add kale and the water; cook until tender, stirring occasionally, about 8 minutes. Add lemon juice and salt, and season with pepper; stir to combine.
Spread each slice of bread with half of the cheese. Top with kale mixture, dividing evenly.
Heat remaining 1 tablespoon oil in another skillet over medium burner. Crack eggs into skillet, one at a time. Cook until whites are just set, about 2 minutes. With a spatula, carefully place an egg on each bruschetta, and serve.