Marinate the olives:

Place quartered olives, olive brine, vodka, vermouth, and lemon peel strips in a small jar or other airtight container. Seal the container and shake well to combine. Let marinate in the refrigerator until flavors meld, at least 30 minutes or up to 1 day.

Strain olives, reserve the liquid to make a delicious martini.

Make the potatoes:

Preheat the oven to 400F.

Bring a large pot of salted water to a boil. Add the potatoes and cook for 15 minutes; larger potatoes may take a few minutes longer. Drain and allow them to dry for 2-3 minutes.

Transfer the potatoes to a baking sheet. Use a flat-bottomed glass to flatten the potatoes. Drizzle the vinegar and 2 tablespoons olive oil over the top, then season with 1 teaspoon of the salt and ½ teaspoon black pepper.

Roast until golden and crispy, 35-45 minutes, depending on the size of your potatoes. Remove from the oven and drizzle with a tablespoon or two more of vinegar depending on how vinegary you want the potatoes to taste.

Make the creamy whipped cheese base:

While the potatoes roast, combine the crumbled feta and cream cheese in a food processor. Blend until smooth and creamy.

Add the olive oil, olive brine, lemon juice, and minced garlic. Blend again until well combined.

Taste and season with salt and pepper as needed. Blend once more to incorporate the seasoning.

To serve:

Transfer the whipped cream cheese and feta mixture to a serving dish and smooth the top with a spatula. Pile the smashed potatoes on top, then top those with the olive mixture and minced parsley. Serve immediately.