Place a large cast-iron skillet in the oven and preheat to 425 degrees F. Rub the pork with 1 tablespoon hot mustard and season generously with salt and pepper; let marinate 5 minutes. Meanwhile, heat the rice as the label directs; set aside.
Carefully remove the hot skillet from the oven, add 1 tablespoon olive oil and swirl to coat. Add the pork, return to the oven and roast, flipping once, until a thermometer inserted into the middle registers 140 degrees F to 145 degrees F, 22 to 25 minutes. Transfer to a cutting board and let rest.
Meanwhile, heat 1 teaspoon olive oil in a large nonstick skillet over high heat. Add the cabbage and a big pinch of salt. Let sit, undisturbed, 1 minute, then toss and cook until crisp-tender and lightly charred, about 1 more minute. Remove to a plate.
Reduce the heat to medium high and add the remaining 1 teaspoon olive oil and the carrots. Cook until just tender, about 6 minutes. Whisk the garlic, soy sauce, brown sugar and remaining 1 teaspoon hot mustard in a small bowl, then add to the skillet with the carrots. Toss to coat; season with salt and pepper. Add the bean sprouts and toss until warmed through, about 1 minute; remove from the heat.
Thinly slice the pork. Divide the rice among bowls and top with the cabbage, carrot mixture, pork and wonton strips.