In batches, pulse the cauliflower in a food processor until rice-size crumbs form. Transfer to a bowl and set aside.
Put a large skillet over medium heat and add the vegetable oil and sesame oil. Add two-thirds of the green onions, the garlic, ginger and chili paste. Cook, stirring constantly, until fragrant, 2 to 3 minutes. Raise the heat to medium high and add the carrots and spinach; continue to cook, stirring, until the spinach has wilted, 1 to 2 minutes.
Continuing to stir constantly, add the cauliflower rice. Cook until the cauliflower is tender, 3 to 4 minutes. Pour in the soy sauce and stir, scraping the bottom of the skillet, until the liquid has evaporated, 2 to 3 minutes longer.
Meanwhile, melt the butter in a second skillet over medium heat. Crack in the eggs; as they cook, spoon hot butter over the whites of the eggs so that the whites set without flipping. Towards the end of cooking, carefully spoon hot butter over the yolks and cook until the eggs reach the desired doneness.
Remove the pan with the cauliflower from the heat, drizzle with sriracha, and sprinkle with the toasted sesame seeds and reserved green onions. Divide between 4 plates and top each serving with an egg.