Place the peas and potatoes in a medium saucepan. Cover them with salted water and bring to a boil over high heat. Reduce the heat and simmer for about 20 minutes, or until both are tender.
While the vegetables are cooking, prepare a 1-quart bowl of ice water with a strainer suspended in it.
Drain the cooked peas and potatoes. Transfer the potatoes to a separate bowl.
Immediately place the peas in the strainer and submerge them in the ice water to chill. Once chilled, drain them and set aside at room temperature.
Return the potatoes to the saucepan. Add the butter and crème fraîche (or olive oil, if using) and heat gently for about 5 minutes, allowing them to warm through.
Add the peas to the saucepan and continue to cook for another 5 minutes.
Remove the pan from the heat, stir, and season with salt and freshly ground black pepper. Shower with the parsley and basil, and serve immediately.