This Eggy Breakfast Burger Features an In-N-Out-Inspired Sauce

Ingredients

• 3 Tbsp. mayonnaise
• 1 Tbsp. dill pickle relish
• 1 Tbsp. ketchup
• 1/2 tsp. sugar
• 1/4 tsp. paprika
• 1/4 tsp. white vinegar
• 4 oz. ground beef, preferably 80 percent lean
• Kosher salt and freshly ground black pepper
• 2 tsp. vegetable oil, divided
• 1 Tbsp. mayonnaise, plus more for serving
• 2 hamburger buns
• Torn lettuce and sliced tomato, for serving
• 2 tsp. yellow mustard
• 2 American cheese slices
• 2 large eggs