Ahh, evolution of our culinary experiments. Disaster struck the first time I tried these plantains, as evidenced by the charred little nuggets that came out. But after consulting with my mom, who can whip them up perfectly every time, and lots of internet recipes, I finally managed to NOT overcook them.
I waited until the plantains were very ripe, almost completely black. I sliced them into 1/4-inch thick diagonals. I poured some canola oil (not corn oil) in the skillet and set it to medium high.
I fried the plantains for about 2-3 minutes per side until they were a nice golden brown. Then I drained them on paper towels.
They were great! Now I just need to figure out how to make them sweeter without overpowering the sweetness of the fruit.