Preheat oven to 425°. Brush sweet potato halves all over with extra-virgin olive oil, then place, cut sides down, on an oven- and microwave-safe 8-in. square pan. Microwave on high until tender when poked with a sharp knife.
When potato halves are cool enough to handle, scoop 1/4 cup potato flesh from middle of each, creating wells for the eggs. Lightly brush potato halves all over with olive oil and sprinkle with salt and pepper to taste. Place skin sides down in pan.
Crack 1 large egg into each potato half and bake until eggs have set and yolks are still runny, 10 to 12 minutes.
Brush potato and egg with cooking juices from the baking dish. Season with salt and pepper to taste, drizzle with Sriracha, and top with cilantro leaves.