In a small pot (about 2-quarts) over medium heat, heat the oil. Add the garlic slices and zest half of the lemon in the oil using a microplane and avoiding the white lemon pith. Cook for 1 to 2 minutes until fragrant or until the garlic is slightly golden on the edges.
Carefully add the bone broth to the pot and bring to a simmer. Season with a hefty pinch of salt.
Crack the eggs in a separate bowl, while keeping the yolk intact. Gently stir the soup to create a vortex in the center. Drop the eggs down the vortex and poach for 2 minutes, until the egg white is opaque, but the egg yolk is wobbly to the touch.
Add the eggs to a serving bowl and pour the soup on top. Squeeze half of the lemon in, plus more to taste.
Sprinkle with parsley, if using, and serve right away.