Beef Burgers with Sweet-n-Smoky Ketchup

Preheat the oven to 350 °. In a medium skillet, toast the chiles over moderately high heat, pressing with a spatula and turning once, until fragrant, about 1 minute. Transfer the chiles to a heatproof bowl and cover with very hot water. Let stand for 30 minutes, until the chiles are completely rehydrated. Meanwhile, on a large rimmed baking sheet, toss the plum tomatoes, garlic, jalapeño and onion with the 1 tablespoon of olive oil and season with salt and pepper. Bake for about 20 minutes, until the vegetables are just soft; let cool slightly. Peel the garlic. Drain the pasilla chiles and transfer to a blender. Add the plum tomatoes, garlic, jalapeño, onion, vinegar and molasses and puree. Season the ketchup with salt and pepper and transfer to a bowl. Refrigerate until chilled. Light a grill or preheat a grill pan. Brush the eggplant and beefsteak tomato slices with oil and season with salt and pepper. Grill over moderately high heat, turning once, until lightly charred. Transfer to a plate. Form the ground beef into 4 burgers, 1/2 inch thick; brush with oil and season with salt and pepper. Grill over moderately high heat, turning once, until the burgers are lightly charred and medium-rare, 7 minutes. Spread the ketchup on the buns. Top with the lettuce, burgers, grilled eggplant and tomato and serve, passing any additional ketchup at the table.