Preheat the oven to 325°F

Place a skillet over medium heat and toss the anise seeds in the dry skillet. Stir constantly for 60 to 90 seconds or until fragrant and toasted. Remove from the skillet, crush, and set aside for later.

Cut the feathery leaves off the fennel bulbs and set them aside.  Slice the fennel bulbs into quarters, leaving some of the core attached to keep the fennel from falling apart.

Add the oil to a skillet set over medium heat. When the oil is hot, place the fennel quarters, cut side down.  Cook the fennel quarters until lightly browned, 2-3 minutes.  Flip the fennel over and cook for 1-2 minutes. 

Remove the skillet from the heat, add the slices of garlic and allow to cook in the residual heat until fragrant, then transfer to a baking dish or oven-proof skillet.  

Sprinkle the surface of the fennel with the toasted fennel seeds, salt, and pepper.    

Pour the wine and chicken broth into the pan, around the edges, not directly on the fennel.  Tuck the thyme sprigs and star anise into the liquid.  

Cover the dish with foil or a lid and transfer to the oven.  Cook in the oven for 60 to 75 minutes or until the core of the fennel is tender.  

Remove from the oven, transfer to a serving dish, drizzle the balsamic vinegar over the fennel and garnish with the leftover fennel fronds.