Once again found a pattern on Ravelry that I just had to make. This is the Chunky Crocheted Basket by Elizabeth Trantham, pattern found here. I used Lion Brand Wool-Ease® Thick & Quick in the color Oatmeal, two strands held together for structure.
The pattern is a bit hard on the hands since it's supposed to be worked tight, but it does come together really quickly. I see more of these baskets in my future. Definitely going to give it a try with t-shirt yarn.