Heat the olive oil in a large pot over medium heat. Add the pancetta and cook until browned and crisp, 7 to 8 minutes. Remove to a paper towel-lined plate, reserving the drippings in the pot. Add the spring onions (white and pale green parts) and carrots and cook, stirring, until tender, 2 to 3 minutes. Add the farro and cook, stirring to combine, about 1 minute.
Add the chicken broth, 4 cups water, 1 teaspoon salt, a few grinds of pepper and the parmesan rind; cover and bring to a simmer. Cook, partially covered and adjusting the heat if necessary, until the farro and vegetables are tender, about 8 minutes. Stir in the zucchini and snap peas and cook until tender, 3 to 4 more minutes. Stir in the basil and lemon zest; season with salt and pepper.
Divide the soup among bowls. Top with the reserved spring onion greens, the grated parmesan, pancetta and a drizzle of olive oil; sprinkle with pepper.