1. Heat oil and butter in a large skillet over medium-high heat. Add mushrooms, kosher salt, and pepper. Cook for 3 minutes or until mushrooms are just tender. Add vinegar. Cook and stir for 2 minutes or until most of liquid has evaporated. Set aside.
2. Shape beef into 8 thin patties 3-1/2 to 4 inches in diameter. Place 1/4 of the mushroom mixture in center of 4 of the patties. Top with remaining patties. Pinch together edges of each double patty, making sure all edges are well-sealed.
3. Place burgers on the lightly oiled rack of the grill directly over medium heat. Grill for 12 minutes; turn. Brush burgers with 1/4 cup of the Latino Barbecue Catsup. Grill 12 to 14 minutes more or until an instant-read thermometer inserted into the center registers 160 degree F. Toast buns on grill, if desired. To serve, place the burgers on the buns. Pass remaining Latino Barbecue Catsup. Makes 4 burgers.
Latino Barbecue Catsup: Combine 1 cup chopped green onions, 1/4 to 1/2 cup chipotle peppers in adobo sauce, 1 jalapeno pepper, chopped; 2 cloves garlic, minced; 1 tablespoon snipped fresh oregano, and 1/2 teaspoon salt in a food processor bowl. Cover; process until combined. Add 1 cup catsup, 1/4 cup red wine vinegar, and 2 tablespoons olive oil; process until smooth. Makes 1-2/3 cups.
Test Kitchen Tip: You can prepare the Latino Barbecue Catsup up to 3 days in advance, then cover and chill it until using.