To quick-soak the beans, put them in the pressure cooker and cover with 3 inches of water. Cover and bring to high pressure. Turn off the heat and let the pressure release naturally, about 5 minutes. Uncover and let cool, about 20 minutes.
Drain and rinse the beans. Return them to the pressure cooker. Add the pancetta, garlic, carrot, rosemary and 1 tablespoon of the olive oil. Add 3 cups of water and bring to a boil. Cover and close the pressure cooker according to the manufacturer's instructions. Cook over very low heat, maintaining high pressure for 7 minutes. Let the pressure release naturally, then uncover and drain the beans.
Transfer the beans to a large, wide bowl or deep platter. Add the lemon juice and remaining 1/4 cup of olive oil and season with salt and pepper. Arrange the trout on top, sprinkle with the parsley and serve right away or at room temperature.