After doing some research online, I found out you can use regular Sharpies to draw on porcelain mugs. You don’t need an oil-based Sharpie or a porcelain pen, but I’m sure one of those would be more suited for the job.
After I drew my design, I baked the mug in a toaster oven at 350 for half an hour, then let it cool. So far, it’s held up to gentle hand washing, but I don’t trust it enough to run it through the dishwasher. Another thing I noticed was that after I baked my mug, the colors of the design came out slightly different than the original Sharpie. It was a bit annoying, because my 3 different colors looked more like 2 different colors, but that can’t be helped. I’m still very happy with the final product. This project is so easy, and there’s so much room for creativity!