Prepare the Fennel: Pick some leafy fronds from the tops and reserve for garnish; trim and discard stalks. Peel away any bruised outer layers. Cut the bulbs in half lengthwise, then cut each half into three equal wedges (similar to orange sections).
Sear the Bulbs: Heat a large pan and add the olive oil. Once the oil is warm, briefly remove the pan from the heat. Arrange the fennel wedges in a single layer in the pan and season with the salt and red pepper flakes.
Brown the Sides: Return the pan to the heat and cook undisturbed until the fennel is light brown on the first side (about 3–5 minutes). Flip the wedges and brown the other side.
Deglaze: Once browned, remove the pan from the heat again to add the white wine and bay leaves. Return to the heat.
Braise until Tender: Simmer over a low flame until the wine has fully reduced. Test the fennel with a knife; if it isn't tender yet, add ½ cup of water and cook until evaporated (another 3–5 minutes).
Finish and Serve: Discard the bay leaves. Stir in the golden raisins and apple cider vinegar, cooking for 2–3 minutes to allow the flavors to integrate. Garnish with the reserved fronds before serving.