Preheat oven to 325F.
In a mixing bowl combine the fennel, salt, honey and orange peel and mix well to coat.
Transfer to a oven safe baking dish and cover with oil. Spread tarragon around evenly. Cook in the oven for 40 minutes until fork tender but not falling apart. Remove and let cool.
Using a slotted spoon, discard tarragon and transfer the fennel to an air tight container. Pour the cooking oil on top, seal and refrigerate for up to 2 weeks.