Place lamb in large bowl. Sprinkle garlic and salt over. Gently toss lamb to blend. Combine feta and mint in small bowl.

Divide lamb into 12 equal mounds. Using damp hands, shape each into ball. Working with 1 ball at a time, poke thumb into center to make hole. Press 1 teaspoon feta-mint filling into hole. Pinch hole closed, then press ball between palms to flatten into 3/4-inch-thick disk. Repeat with remaining lamb and feta-mint filling. DO AHEAD: Can be made 1 day ahead. Transfer to baking sheet. Cover and refrigerate.