Preheat the oven to 350F (180C).
Trim the fennel and cut off the base. Cut each fennel bulb into quarters. Peel the potatoes and quarter them lengthwise.
Use a heavy saucepan that is oven-safe, and warm it on the stove at medium-heat. Add the olive oil and butter and heat until the butter has melted.
Add the fennel and potatoes. Season with a little salt and cook for 10 minutes or so.
Add the bay leaves, sage, and garlic. Crumble in the dried red chili, and stir to combine.
Roughly chop the tomatoes and add to the pan, along with the chopped preserved lemon, then pour over the broth.
Cover and bake in the oven for 40 minutes, or until the fennel is very tender, adding the olives for the last 5-10 minutes.
Taste and adjust the seasoning then spoon over the basil oil, and scatter over some sage leaves to garnish. Sprinkle with grated parmesan and serve.