Step 1. Put the pasta onto a frying pan.
Step 3. Turn the water on high and boil for 15 minutes, turning pasta occasionally.
Result: This method worked well to cook the noodles and it was faster than boiling water in a pot. The downside was that with the shallow frying pan, water splattered onto the stove every time I turned the noodles. I wonder if this would work better in a flat pan with higher sides. I might try that next time.
My tweaks: I was running late with dinner so the liquid from the tomatoes in my pasta sauce wasn't done cooking down yet.
I decided that I could move the process along by adding the pasta into the sauce for the last 5 minutes of the pasta cooking time, figuring the starch from the pasta would absorb the water and maybe the noddles would take on some of the sauce flavor.