Preheat an oven to 325 degrees. In a soup pot over low heat, warm the olive oil. Add the garlic and cook slowly, stirring occasionally, until the oil is well flavored and the garlic is soft but has not begun to color, about 5 minutes. Remove from the heat and discard the garlic cloves.
Place the bread cubes in a bowl and pour about half of the garlicky oil over them (leave the remaining oil in the pot). Toss well to coat, sprinkle with the salt and pepper, and spread out on a baking sheet. Bake until golden brown and crisp throughout, 10-15 minutes. Remove from the oven and set aside.
Pour the stock into the soup pot holding the remaining oil. Place over medium heat and bring to a simmer. Gradually add the eggs to the simmering stock while stirring the stock constantly in a circular motion. Add the epazote or oregano and simmer until the eggs are set, about 3 minutes longer. Remove from the heat.
Divide the croutons among 6 warmed soup bowls and ladle the egg-laced stock into them. Squeeze a wedge of lime over each bowl, then drop the wedge in the bowl. Serve immediately.