Place quartered olives, olive brine, gin, vermouth, and lemon peel strips in a bowl. Let marinate in the refrigerator until flavors meld, at least 30 minutes or up to 1 day.
Strain olives, reserving the olives and brine mixture separately.
In a medium bowl, using an electric hand mixer, beat together cream cheese, blue cheese, salt, pepper, and 5 tablespoons of the reserved brine mixture mixer on medium speed until well blended. Taste and stir in additional brine mixture, if desired.
Transfer cheese mixture to a small serving bowl. Pour 2 tablespoons of the olive oil into the center. Spoon reserved marinated olives over top. Drizzle with remaining 1 tablespoon olive oil and sprinkle with flaky salt and pepper. Serve with crostini.