Wash and dry all produce. Adjust rack to top position and preheat oven to 425 degrees. Peel ginger, then mince or grate until you have 1 TBSP. Peel carrots, then slice on a deep diagonal into 1/2-inch-thick spears. Halve lime.

In a small bowl, stir together hoisin sauce, sriracha, sesame oil, a squeeze of lime juice, and 2 TBSP water; set aside. Toss carrots with a drizzle of vegetable oil on a baking sheet. Season with plenty of salt and pepper. Roast in oven until tender, about 20 minutes, tossing halfway.

Melt 1 TBSP butter in a small pot over medium-high heat. Add minced ginger and cook, stirring, until fragrant, 1-2 minutes. Add 13/4 cups water and a pinch of salt (about 1/4 tsp). Bring to a boil, then stir in rice and return to a full boil. Lower heat, reduce to a gentle simmer, and cover. Cook until tender, 15-20 minutes. Keep covered off heat.

Meanwhile, mix together panko, garlic powder, half the sesame seeds, and a large pinch of salt on a plate. Pat pork dry with a paper towel, then season all over with salt and pepper. Brush pork with sour cream, coating evenly. Working one cutlet at a time, dip pork into panko mixture, flipping to coat and pressing to adhere. Set finished cutlets aside on another plate while you work with the rest.

Heat a 1/4-inch layer of vegetable oil in a large, preferably nonstick pan over high heat. Once very hot, add half the pork and cook until crust is golden brown and meat is cooked through, 2-3 minutes per side. (TIP: Lower heat if crust browns too quickly.) Transfer to a paper-towel-lined plate and immediately season with salt. Repeat with remaining pork.

Fluff rice with a fork, then stir in a big squeeze of lime juice. Season with salt and pepper. Divide rice, carrots, and pork between plates. Sprinkle with remaining sesame seeds. Drizzle sauce over pork (or serve it on the side for picky eaters).