To prepare the ketchup: Preheat the oven to 350 degrees F. Toss the tomatoes in 1 tablespoon of the olive oil and place on a baking sheet. Roast in the oven for 10 to 15 minutes or until soft.
Transfer the tomatoes to a food processor and process until smooth. Strain the tomatoes, pressing against the solids with a wooden spoon to extract as much pulp and juice as possible.
Heat the remaining olive oil in a medium saucepan over medium heat and saute the onions and garlic until translucent. Add the tomato puree and remaining ingredients and continue cooking, uncovered for 25 to 30 minutes, stirring occasionally until thick.
To prepare the burgers: Shape the meat firmly into 4 round uniform patties about 1 1/2-inches thick. Brush both sides of the burgers lightly with the remaining olive oil and season with salt and pepper to taste. Heat a large cast iron skillet over medium high heat until just smoking. Cook the burgers until done to your preference, 5 to 6 minutes on each side for medium rare etc.