Preparation Melt butter in a large skillet over medium heat. Cook onion, garlic, and red pepper flakes, stirring often, until onion is softened and translucent, about 4 minutes. Add orzo and stir until coated in butter, about 30 seconds. Add tomatoes and juices and cook, stirring, until liquid is reduced and tomatoes are starting to stick to skillet, about 4 minutes. Add salt and 2 cups water, increase heat to medium-high, and bring to a simmer. Reduce heat to low, cover pan (a baking sheet works well if you don’t have a lid), and cook 8 minutes, stirring halfway through. Uncover and simmer 1 minute—mixture should be fluid but not watery. Stir again, then remove from heat and crack each egg into a quadrant of pan. Cover pan, set over low heat, and cook, rotating pan every 2 minutes or so, until eggs are nearly set, about 5 minutes. Sprinkle cheese over, avoiding eggs, cover pan, and cook until cheese is melted, about 2 minutes. Remove from heat and top with a few grinds of pepper and basil to serve.