Better Turkey Burger with Feta and Onion Jam

Name: Better Turkey Burger with Feta and Onion Jam
Ingredients: 1 large yellow (or vidalia) onion; 1 tablespoon olive oil; 1 teaspoon paprika; 1/2 teaspoon soy sauce; 1 splash red wine; 1 pound lean ground turkey; 1 teaspoon cumin; 1 teaspoon garlic powder; 1 teaspoon each salt and pepper; 4 brioche buns; 8 ounces feta cheese, cut into slices; 1 arugula; 1 large tomato, sliced thick