Prep: 5 minutes; Cook: 10 minutes.
1. Heat a large cast iron or heavy-bottomed skillet over medium-high heat. Sprinkle steak with fennel seeds, 1/2 teaspoon salt, and 1/2 teaspoon pepper. Add 1 tablespoon oil to skillet. Cook steak in hot oil, turning once, about 3 minutes on each side for medium-rare.
2. While steaks cook, cut fennel in half, and remove tough outer layers. Remove core, and slice very thinly. Chop 1 tablespoon fresh fennel fronds, and place in a medium bowl with sliced fennel. Zest lemon into a small bowl; cut lemon in half, and add 1 teaspoon juice. Add remaining 1/4 teaspoon each salt and pepper; set aside.
3. Transfer steak to a cutting board, and cover loosely with aluminum foil to keep warm.
4. Add butter and remaining 1 tablespoon oil to skillet. Add fresh fennel, and cook about 30 seconds. Add lemon mixture; cover and cook, stirring occasionally, 4 minutes or until fennel is crisp-tender. Cut steak into thin slices, and serve with fennel mixture.