Preheat oven to 400° F
Remove stalks from the fennel and trim the bottom. Discard the stalks (or save to make vegetable broth later!) Slice each fennel bulb in half lengthwise, and then slice each half into ½” slices. Spread the slices on a baking sheet in a single layer.
Drain the artichoke hearts, slice in half lengthwise and pat dry. Arrange on the baking sheet along with the fennel, making sure that nothing overlaps.
In a small bowl, combine oil and garlic, and brush it over the fennel and artichoke slices. Sprinkle each slice with thyme, salt and pepper.
Roast for 25-30 minutes before sprinkling each slice with parmesan cheese. Continue to roast for another 10 minutes, until the fennel and artichokes are tender and caramelized. Serve immediately.