How to Make It
Preheat oven to 350°F. Place phyllo shells on a rimmed baking sheet. Bake until crisp, 5 minutes. Cool completely, 15 minutes.
Combine cream cheese, garlic, 4 ounces of the feta, 2 tablespoons of the oil, 1 1/2 teaspoons of the vinegar, 1/4 teaspoon of the salt, and 1/4 teaspoon of the black pepper in a food processor. Process until smooth, about 1 minute, stopping to scrape down sides as needed. Transfer feta mixture to a ziplock plastic bag. Cut a 1/2-inch hole in 1 corner of the bag. Pipe about 1 tablespoon feta filling into each phyllo cup.
Stir together cucumber, bell pepper, parsley, oregano, and remaining 1 ounce feta, 1 tablespoon oil, 1 1/2 teaspoons vinegar, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Spoon about 1/2 tablespoon relish into each phyllo cup.