Preheat the oven to 325 degrees. Heat the olive oil over a low flame in a soup pot and add the halved garlic cloves. Cook slowly, stirring occasionally until oil is well flavored and garlic is mushy, but has no color, about 5 minutes. Remove and discard the garlic. Pour about half the oil over the diced bread in a bowl and toss well to coat. Sprinkle well with salt and pepper and spread out on a cookie sheet. Bake for 10 to 15 minutes, or until golden brown and crisp through, and set aside.
Pour the broth into the pot with the remaining garlicinfused oil and heat to simmering. Lightly beat eggs again and, stirring constantly in a circular motion, add them to the broth. Add epazote and simmer until eggs are set, about 3 more minutes. Divide croutons among 6 warm soup bowls and ladle egg drop broth into each bowl. Garnish with a squeeze of lime and drop the lime wedge in the bowl. Serve immediately.
