Curry Pork Burgers with Spicy Ketchup

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For the patties:

2 1/2 pounds ground pork, crumbled

2 teaspoons ground coriander 

2 teaspoons yellow curry powder 

2 teaspoons Worcestershire sauce 

1 teaspoon cayenne pepper 

3 scallions, finely chopped (white and green parts) 

2 garlic cloves, finely chopped 

2 1/2 teaspoons kosher salt 

Freshly ground black pepper 

2 tablespoons olive oil, plus more for cooking the burgers

For the spicy ketchup:

1/2 teaspoon crushed red pepper flakes

1 garlic clove, grated on a rasp or finely minced 

1 tablespoon unsalted butter 

1 cup ketchup 

1/4 teaspoon cayenne pepper 

1 scallion, finely chopped (white and green parts) 

For the burgers:

6 potato hamburger buns

1 head Boston, Bibb, or other butter lettuce 

2 Roma tomatoes, sliced lengthwise