Prepare a baking dish with olive oil coating the bottom. Preheat the over to 450 convection bake.
Trim the spikey part off the artichoke leaves. Cut the stem to about one inch.
Cut the artichokes in half. Use a spoon to dig out the internal layer where the leaves change texture.
Take your peeled garlic cloves plus a sprig of rosemary and stuff inside the artichoke. Place the artichokes face down on the baking dish. Put in the oven uncovered for about 15 minutes or until the outside of the artichoke is beginning to crisp.
Add the asparagus to the baking dish. Cover the baking dish with a sheet of aluminum foil. Turn oven to bake at 450. Leave cooking for about 15 minutes or until a fork easily slides into the stem (pointed up toward the leaves) of the artichoke.