Method:
Heat a large sauté pan over medium heat. Add oil, garlic, peppers and onions and cook, stirring occasionally, until onions are translucent, about 5 minutes. Stir in tomatoes, salt, chile powder, garlic powder and cilantro; simmer for 10 minutes.
Stir in lime juice and vinegar.
Carefully purée sauce in blender, in batches if necessary, then return to pan. Add enough broth to thin out the sauce, then bring to a simmer. Crack eggs into sauce, leaving space between each egg. Cover and poach eggs until egg whites are opaque and yolks are light yellow, about 10 minutes.
Transfer to plates and serve topped with avocado and cheese. Garnish with cilantro and lime wedges and serve with hot sauce and tortillas on the side.