Add the flour, salt and baking powder to a food processor and pulse to combine. Toss in the cold butter cubes and pulse until the mixture resembles coarse bread crumbs.
Add milk, a little bit at a time until it is completely worked into the dough. Once it comes together into a nice consistent ball and pulls away from the sides of the food processor, divide the dough into about 12 little balls. Push a slice of plantain into the middle of each ball and pinch the dough around the plantain so it is completely covered by the dough. Press each ball flat into a little cake, cover with a damp kitchen towel and allow to rest for 20 to 30 minutes before frying.
Set a large nonstick skillet over medium heat and add 1/4 cup of vegetable oil. Prick the dumplings all over with a fork. Working in batches, pan-fry dumplings until golden and slightly puffy, about 3 to 5 minutes per side. Season with salt and serve warm.