Combine salt, ground fennel seeds, ground cumin, and black pepper in a small bowl.
Heat 2 teaspoons oil in a large nonstick skillet over medium-high heat. Add 1/2 teaspoon spice mixture and fennel; sauté 15 minutes or until fennel is tender and lightly browned. Transfer to a bowl; wipe pan clean with paper towels.
Heat remaining 2 teaspoons oil in pan; sprinkle steaks evenly with remaining spice mixture. Add steaks to pan; cook 4 minutes on each side or until desired degree of doneness. Remove from pan; let stand 10 minutes. Thinly slice steaks.
To prepare sandwiches, spread 2 teaspoons mayonnaise onto each of 4 bread slices. Top each with one-fourth of beef, one-fourth of fennel, and 1/4 cup arugula. Top with remaining 4 bread slices.
Cooking Tip When buying fennel, look for small, heavy, white bulbs that are firm and free of cracks, browning, or moist areas. The stalks should be crisp, with feathery, bright-green fronds. Wrapped in plastic, fennel keeps for just a few days in the refrigerator; the flavor fades as it dries out.