How to Make It
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.
The ketchup can be refrigerated for up to 1 week.