Preheat the oven to 350 degrees F.
Slice off the top part of the tomatoes horizontally and scoop out the pulp and seeds. Reserve for another use. Season the tomatoes heavily with salt and pepper.
Heat the oil in a medium saute pan over medium-high heat. Add the potatoes and cook until crisp, about 6 minutes. Transfer the potatoes to a plate lined with a paper towel to drain off excess oil. Add the chorizo to the pan and cook for about 3 minutes. Transfer the potatoes back to the pan with the chorizo. Keep cooking until the chorizo is crisp, about 3 more minutes. Season to taste with salt and pepper. Remove from heat and drain off excess fat on a paper towel.
Divide the chorizo mixture evenly between the scooped out tomatoes. Crack one egg onto each of the tomatoes. Place the tomatoes in a baking dish and bake for about 25 minutes or until the egg whites are fully cooked. Crumble queso fresco on top and sprinkle with cilantro. Serve immediately.