Prepare the vegetables. Have ready a medium-size saucepan of boiling salted water. Add the potatoes and cook until tender, about 12-15 minutes. Lift out, letting them drain well, and peel. Set aside.
Add the diced carrots and cook until crisp-tender, about 4 minutes. Scoop out with a strainer or slotted spoon and set aside.
Add the peas and cook until barely tender, about 3 minutes. Remove and drain.
In a large bowl, mash the potatoes with a potato masher. Add the crema and beat with a wooden spoon to eliminate most of the lumps. Add the egg and mustard, continuing to beat until the mixture is smooth and fluffy.
Preheat the oven to 350°F.
In a medium-size skillet, melt the butter over medium-high heat until fragrant and sizzling but not browned. Add the onion and garlic and cook, stirring, for 3 minutes, until the onion is translucent. Add the parsley, cook for 1 minute longer, and beat the mixture into the mashed potatoes. Stir in the diced carrots, peas, pickled onions, olives, and jalapeños. Taste for seasoning and add the pepper and optional salt.
Transfer the mixture to a buttered 2-quart baking dish and bake 20 minutes. Serve at once.