Dirty Martini Dip

Ingredients

3/4 cup pitted Castelvetrano olives (from 1 [16-ounce] jar), drained and quartered lengthwise
1/4 cup olive brine (from 1 [16-ounce] jar)
1/4 cup (2 ounces) gin
1 tablespoon dry vermouth
3 (3- x 1-inch) strips lemon peel (from 1 lemon)
12 ounces cream cheese (from 2 [8-ounce] packages), slightly softened
4 ounces creamy blue cheese
1/4 teaspoon kosher salt
1/8 teaspoon black pepper, plus more for garnish
3 tablespoons extra-virgin olive oil, divided
Flaky sea salt, for garnish
Crostini, for serving