Drain the artichokes and squeeze out as much water as possible. Place them on a paper towel and let dry out.
Drain the chickpeas and rinse them.
Cut the artichokes into half, lengthwise, or quarters if very large. Try to keep the pieces intact.
In a large iron skillet, heat the oil over medium-high. Mince the garlic and add to the pan.
Add the artichoke hearts and let them sit on the pan for about 30 seconds to brown. With a spatula, gently turn them and brown some more. You want to let them roast, so don't turn too often. When they have some nice brown edges, add the chickpeas and turn down the heat to medium.
Add the paprika and thyme and toss gently. Let the chickpeas also get a little crispy. Turn the heat to low and cook another 5 minutes. Grind some pepper over the top. Taste for salt, but you won't need much.
You can make this ahead and gently reheat. Serve hot or room temperature. Experiment with other spices, like ground chile and oregano.