Wash and dry all produce. Halve zucchini lengthwise, then cut crosswise into half-moons. Trim and thinly slice mushrooms. Trim and thinly slice scallions, separating whites from greens. Using a peeler, shave carrot lengthwise into ribbons, rotating until you get to the core. Discard core. Peel and mince or grate ginger.

Melt 1 TBSP butter in a small pot over medium-high heat. Add ginger and cook, stirring, until fragrant, about 2 minutes. Stir in rice, 11/4 cups water (21/4 cups for 4 servings), and a pinch of salt. Bring to a boil. Once boiling, cover and reduce heat to low. Cook until water has absorbed and rice is tender, about 15 minutes.

Meanwhile, in a small bowl, combine scallion whites with vinegar and a pinch of salt; set aside to marinate. In a second small bowl, combine sesame oil, 1 TBSP sugar (2 TBSP for 4 servings), up to 1 tsp sriracha, and soy sauce.

Heat a drizzle of oil in a large pan over medium-high heat (use a nonstick pan if you have one). Add carrot and season with salt and pepper. Cook, stirring, until just tender, 3-4 minutes. Transfer to a medium bowl. Add zucchini and another drizzle of oil to pan. Cook, stirring, until tender, 5-6 minutes. Transfer to bowl with carrot. Add mushrooms and another drizzle of oil to pan. Cook, stirring, until tender, 3-5 minutes. Season with salt and pepper. Transfer to bowl with other veggies. Wipe out pan.

Heat 1 TBSP oil in pan used to cook veggies over medium heat. Once hot, crack eggs into pan and cover. (For 4 servings, you may want to cook eggs in batches.) Cook until whites are set but yolks are still runny, about 3 minutes. Season with salt.

Fluff rice with a fork and season with salt and pepper; divide between bowls. Arrange carrot, zucchini, and mushrooms on top. Top with eggs and pickled scallion whites (draining, if necessary). Drizzle with sauce and any remaining sriracha (to taste). Sprinkle with scallion greens and serve.