Place 4 cups warm water into a large bowl. Stir in about 1 tablespoon of salt. Set aside.
Peel the plantains. (The easiest way to do this is to cut the ends off, then run your knife through the peel lengthwise on two sides – without piercing the actual flesh. Use the knife to get under the skin and peel it off.)
Cut plantains crosswise into 1-inch thick pieces. Place in bowl of warm salted water. Let sit 15-20 minutes. (This step adds flavor & also gets rid of some of the starch from the plantains.)
Heat oil over MEDIUM heat until the oil is glistening. You’ll know it’s hot enough when a small "tester" piece of plantain sizzles.
Remove plantain pieces from the water & blot completely dry with paper towels.
Place plantain pieces in the oil (don’t crowd the skillet; it’s better to do 2 batches if needed). Fry plantains 5-7 minutes, turning occasionally with tongs, until tender & just beginning to turn golden color.
Remove plantain pieces with tongs to a flat, non-stick surface, such as a cutting board. For safety, remove pan from flame.
Spray the bottom of a heat-proof glass tumbler or mug with non-stick cooking spray. Gently flatten each plantain piece to ~1/4" thickness. Small cracks are OK. Slide plantain off glass.
Reheat oil over medium heat and return flattened plantains to hot oil. Fry 3-4 minutes, turning occasionally, until plantains are golden brown in color.
Transfer plantains to a plate with a fresh paper towel, but DO NOT BLOT. Sprinkle with salt & serve immediately, with ketchup (optional).