1. Bring a large pot of generously salted water to a boil. Cook pasta until al dente. Reserve 1 cup pasta water; drain.

2. Meanwhile, heat a large straight-sided skillet over medium-high heat. Add 1 tablespoon oil and sausage; cook, breaking into pieces, until browned, about 5 minutes. Transfer to a plate. Drain all but 1 tablespoon fat; reduce heat to medium. Add remaining 1 tablespoon oil, fennel, and carrots. Season with salt and pepper. Cook, stirring occasionally, until tender, about 10 minutes. Add broth; bring to a simmer. Add pasta, pasta water, lemon zest and juice, cheese, and sausage. Simmer, stirring, 3 to 4 minutes. Remove from heat; let stand to thicken, about 10 minutes. Drizzle with oil. Serve with fennel fronds, lemon wedges, cheese, and arugula.