Begin by trimming the base of each endive, removing any damaged outer leaves, and slicing them in half lengthwise.
In a large skillet, heat the olive oil over medium heat. Place the endive halves cut-side down into the skillet, and cook for about 3-4 minutes or until they start to brown.
Flip the endives over and add the chicken or vegetable broth, orange juice, orange zest, and star anise to the skillet. Season with salt and pepper to your liking.
Bring the liquid to a simmer, then reduce the heat to low, cover the skillet, and let the endives braise for about 20-25 minutes, or until they are tender.
Once the endives are tender, remove the lid, increase the heat to medium, and allow the braising liquid to reduce slightly, for about 2-3 minutes.
Remove the skillet from the heat, discard the star anise, and stir in the tablespoon of butter until it's melted and the sauce is slightly thickened.
Plate the braised endives, drizzle with the sauce from the pan, and garnish with fresh parsley if desired. Serve immediately.