In a large skillet, melt the butter over medium heat. Add the alliums (shallots, scallions, leeks and onion) and a good pinch of salt and cook, stirring, until everything is nice and soft and smelling really good, 12 to 15 minutes.
Meanwhile, heat a separate skillet over medium-high heat and coat the bottom with a thin layer of oil. When the pan is hot, add the eggs and cook, gently scraping up the bottom with a silicone spatula, until mostly set. Remove the eggs from the heat, season with salt and pepper, give them a rough chop, and set aside. (Alternatively, you could cook the eggs first in the large skillet, then remove them before adding the butter and cooking the alliums.)
Add the garlic and ginger to the alliums and cook, stirring, for 2 more minutes. If the pan looks dry at any time, add a bit more butter or some oil. Add the rice and scrambled eggs and fold to combine. Salt the rice to taste. Increase the heat to medium-high, spread the mixture out evenly over the skillet, and let it cook, uninterrupted, until the bottom is crispy, about 5 minutes. Serve with Sriracha and mayo and remaining scallions.