Preheat oven to 450°F.

Toss fennel, 3 teaspoons oil, chopped thyme and 1/4 teaspoon each salt and pepper in a medium bowl. Spread on a rimmed baking sheet. Roast, stirring twice, until tender and golden, about 25 minutes.

Meanwhile, sprinkle both sides of turkey with the remaining 3/4 teaspoon salt and 1/2 teaspoon pepper. Heat the remaining 2 teaspoons oil in a large skillet over medium-high heat. Add the turkey and cook until browned, 1 to 3 minutes per side. Transfer to a plate.

Add pomegranate juice and thyme sprig to the pan; bring to a boil. Boil, stirring often, until reduced to 1/4 cup, 6 to 10 minutes. Discard the thyme. Whisk together broth (or water) and cornstarch; add to the pan and cook, stirring constantly, until thickened, about 15 seconds. Reduce heat to medium, return the turkey and any accumulated juices to the pan, turning to coat with sauce, and cook for 1 minute. To serve, top roasted fennel with turkey and sauce.