Vidalia Onion Tart

Name: Vidalia Onion Tart
Ingredients: 1 ½ teaspoons extra-virgin olive oil plus 2 tablespoons, divided; 1 ½ pounds sweet onions (about 3 medium), preferably Vidalia, sliced; ½ teaspoon packed dark brown sugar; ¾ teaspoon ground pepper, divided; ½ teaspoon kosher salt, divided; ¼ cup dry red wine; 1 large egg; 1 tablespoon chopped fresh thyme plus 1 teaspoon, divided, and more for garnish; 1/4-1/2 teaspoon crushed red pepper; 20 sheets phyllo dough (9-by-14-inch), thawed per package directions; 2 tablespoons butter, melted; ½ cup crumbled feta cheese