Special equipment: a 12-inch oven-safe nonstick pan and 2 3/4-inch biscuit cutter
Preheat the oven to 400 degrees F.
Using a 2 3/4-inch biscuit cutter, cut holes out of the center of each slice of bread. Reserve the cutouts. Heat the butter in a 12-inch oven-safe nonstick pan over medium heat. Toast the bread and cutouts in the pan for 2 minutes on each side. Add an egg to the hole in each piece of bread and season with salt and pepper. Cook until the egg is slightly set on the bottom, about 2 minutes. Transfer the pan to the oven and bake until the whites are just set and the yolks are still soft, about 5 minutes. Garnish with the desired toppings.
For the chorizo: Heat the vegetable oil in a 12-inch skillet over medium heat. Add the chorizo and cook until rendered and browned on both sides, about 5 minutes total. Remove and set aside. Note: You can use the rendered chorizo fat instead of butter to cook the sourdough slices.
For the tomato salsa: Combine the tomatoes, cilantro, scallions and lime juice in a bowl and season with salt and pepper to taste. Serve with Mexican hot sauce.
For the eggplant: Heat a grill pan over medium-high heat. Cook the eggplant until tender and slightly charred, about 2 minutes per side. Combine the olive oil, vinegar, parsley, red pepper flakes, garlic and salt and pepper to taste in a bowl. Add the grilled eggplant slices and marinate for at least 1 hour at room temperature and up to 1 week in the refrigerator.