Martha's Secret Turkey Burger

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Two 12-ounce jars red-pepper relish, such as Fourth Creek Food Co.

1 small onion, chopped 

2 cloves garlic, chopped 

1 tablespoon plus 1 teaspoon extra-virgin olive oil, plus more for brushing 

2 tablespoons low-sodium soy sauce 

2 pounds ground dark turkey 

4 teaspoons Worcestershire sauce 

1 teaspoon Dijon mustard 

1 slice soft white bread, torn into pea-size pieces (1 cup) 

Kosher salt and freshly ground black pepper 

3 tablespoons chili sauce, plus more for brushing 

1/2 cup mayonnaise 

2 packed cups finely shredded kale 

1/2 teaspoon balsamic vinegar 

8 brioche rolls, split 

4 tablespoons unsalted butter, melted