Ingredients

• 1/4 cup ketchup
• 1/4 cup mayonnaise
• 1 teaspoon Asian chile paste such as sambal oelek
• 1 1/4 pounds ground beef chuck
• 4 kaiser rolls, split
• 4 pineapple rings
• 1 tablespoon vegetable oil, divided
• 4 large eggs
• 3/4 cup drained sliced pickled beets

Instructions

1. Prepare grill for direct-heat cooking over medium-hot charcoal (medium heat for gas); see Grilling Procedure .
2. Combine ketchup, mayonnaise, and chile paste.
3. Mix beef with 1 teaspoon salt and 1/2 teaspoon pepper, then form into 4 (4 1/4-inch-diameter) patties.
4. Lightly toast rolls on grill.
5. Pat pineapple dry and brush with 1/2 tablespoon oil.
6. Oil grill rack, then grill pineapple and burgers, covered only if using a gas grill, turning once, until pineapple is tender and caramelized and burgers are medium-rare, about 4 minutes total.
7. Heat remaining 1/2 tablespoon oil in a large nonstick skillet over medium-high heat until hot, then fry eggs.
8. Spread chile mayonnaise on rolls, then assemble burgers with pineapple, beets, eggs, lettuce, and tomato.