Heat oil in a large ovenproof skillet over medium-high. Sprinkle pork with 1/4 teaspoon salt and 1/4 teaspoon pepper. Add pork to pan; cook 6 to 8 minutes, turning to brown on all sides. Place pan in oven; bake at 400°F for 18 minutes or until a thermometer inserted in the center registers 140°F. Place pork on a cutting board; let stand 5 minutes. Cut crosswise into slices.
Return pan to medium-high (use caution; the handle will be very hot). Add fennel, garlic, and mushrooms; cook 5 minutes or until golden, stirring occasionally. Add stock; bring to a boil. Cook 3 minutes or until liquid is reduced by half. Remove pan from heat; stir in remaining 1/4 teaspoon salt, remaining 1/4 teaspoon pepper, and arugula until wilted. Arrange pork on a platter; top evenly with fennel mixture, cheese, and fennel fronds