Peel the plantains. Cut each plantain into thick wedges.
Frying method: Heat the oil in a medium pot over medium heat. Line a plate with paper towels and set aside.
Fry in batches, turning frequently, until golden brown, about 30 seconds. Remove to the plate lined with paper towels and season immediately with the sea salt.
For baking method: Adjust an oven rack to the lowest position and preheat the oven to 475 degrees F.
Cover a large baking sheet with parchment paper and apply cooking spray. Arrange the plantain fries in a single layer on the baking sheet and cover the sheet tightly with foil. Bake for 5 minutes, then remove the foil and continue to bake for 10 minutes. Rotate the pan and cook another 5 minutes, until the underside of the plantains are spotty golden brown.
Remove the baking sheet from the oven and scrape the fries loose with a spatula. Then use tongs or the spatula to flip over each wedge. Continue to bake until the fries are golden and crisp, about 5 minutes more.