1. Preheat the oven to 250°F, select one or two baking sheets large enough to arrange the tomatoes in one layer and brush with oil. Arrange the tomatoes on the sheets cut side up and sprinkle them lightly with salt. Set aside.

2. Select a heavy roasting pan or large gratin dish for the fennel (it does not have to fit in a single layer), and brush the bottom with oil. Remove any fennel fronds and set aside for garnish. Cut the top stalks from the fennel and reserve for stock. Trim the base, and quarter each bulb, top to base. Discard any tough or bruised outer layers. Slice the quartered bulbs ¼ inch thick, leaving the core as intact as possible to hold the layers together. (This won’t be possible with all of the slices.) Set in the roasting pan, seasoning lightly with salt and drizzling with olive oil as you go. Cover the pan tightly with foil.

3. Bake the tomatoes until collapsed and shriveled, 2 to 2½ hours. (For the first hour or so, it will look like nothing is happening.) At the same time, bake the fennel until tender and easily pierced with the tip of a paring knife, 1½ to 2 hours. (Once the fennel is tender, you can roast it uncovered to brown it and achieve a more intense flavor.)

4. To serve, arrange the fennel and tomatoes decoratively on small plates and drizzle with extra-virgin olive oil. Finely chop the reserved fennel fronds and use them as a garnish. If you wish, dot a few drops of Balsamic Syrup decoratively around the plate.