1. Place 1 1/2 cups broth in a small saucepan and warm over very low heat. Grate one-quarter of the carrots and set aside. Dice remaining carrots and puree in a food processor with remaining broth.
2. Melt butter in a large heavy-bottomed saucepan over medium heat until foaming, about 2 minutes. Add onion, cumin, grated carrots, 1/4 teaspoon salt and 1/8 teaspoon pepper and cook until translucent, about 5 minutes. Add farro and cook, stirring constantly, until it starts to crackle, about 2 minutes. Add wine and cook about 1 minute.
3. Decrease heat to medium low, stir in carrot puree and bring to a simmer. Add 1/2 cup broth and simmer, stirring constantly, until broth is nearly absorbed, about 5 minutes. Continue adding broth 1/2 cup at a time, stirring occasionally, until its absorbed and farro is al dente and has a porridgelike consistency, 25 to 30 minutes.
4. Stir in 1 1/2 teaspoons oil, lemon juice and remaining salt and pepper; cover, remove from heat, and let rest 3 to 5 minutes. Stir in Parmesan, chives and lemon zest. Drizzle with remaining oil.