Heat a large skillet over medium-high heat. Add 3 Tbsp. oil and the carrots, and season with salt and pepper. Cook, stirring occasionally, until carrots just begin to soften, about 5 min. Add the shallots, and continue to cook, stirring more frequently, until carrots are tender and shallots are golden, about 8 min. more. Add the cumin into the carrot mixture and cook, stirring, until fragrant, about 30 sec. Scrape the carrot mixture into a large bowl, and toss with the lemon juice.
Toss the rice with 1/2 cup Parmesan. Return the skillet to medium-high heat, and add the remaining 2 Tbsp. oil. Add the rice to the skillet. Using a wooden spoon or a spatula, compress the rice into a thin layer that covers the bottom of the pan. Let cook until golden on the bottom, about 5 min.
Using a metal spatula, turn the rice in pieces (it's OK if it breaks up). Brown the other side, about 5 min. more. Transfer to the bowl with the carrots, breaking into bite-size pieces.
In a small bowl, combine the remaining 1/4 cup Parmesan, pistachios, parsley, and lemon zest. Add half the Parmesan mixture to the bowl with the carrots; toss to combine. Serve with remaining Parmesan mixture and lemon wedges.
Recipe by Laura Rege.