Pulse the pistachios in a food processor until coarsely chopped. Set aside half of the nuts. Pulse the remaining nuts until they are quite fine but not pasty. Add the parsley and mint, and pulse until the herbs are finely chopped. Add the butter, cheese, zest, Sriracha, and salt. Pulse until a well blended paste.
Combine the carrots and 1 tsp. salt in a 4-quart saucepan and add enough water to just cover. Cover the pan and bring to a boil over high heat. Reduce the heat to maintain a simmer and cook to your liking, about 5 minutes for crisp-tender.
Reserve about 1/4 cup of the cooking water, drain the carrots, and then return them to the pan. Add the butter in pieces and toss to melt and coat the carrots. Add the lime juice and some of the reserved water, if necessary. Season to taste with salt and more lime juice. Serve topped with the reserved pistachios.