I tried to articulate the process to a few people, but ultimately they were confused. So, I decided to illustrate the process and I believe it is much more clear with both words and pictures. See below!
Although my bowties were different sizes, they were a lot of fun to make and eat. I would recommend a lot of flour on the countertop if you try this shape. I had problems with the dough sticking more than usual, which may have been a result of the humid and rainy weather. In the end, I had to throw out a lot of dough.
Look how adorable these bowtie pastas are! I let them dry on cooling racks for a few hours. They cooked in about 6 minutes in salted boiling water.