Score the tomato skins with a sharp paring knife and place them in a bowl of boiling water for 10–15 minutes. Peel away the skins once they loosen easily.
Heat 1 tablespoon olive oil in a large deep pan over medium heat. Add the diced bell peppers and cook for 8–10 minutes until softened and lightly golden.
Stir in the minced garlic and jalapeños. Cook for 1 minute until fragrant but not browned.
Add the peeled tomatoes, grape tomatoes, chili flakes, sugar, and salt. Stir well and bring the mixture to a gentle boil over medium heat.
Reduce the heat to medium-low and simmer uncovered for 65–75 minutes. Stir every 10 minutes until the tomatoes break down and the mixture becomes thick and jammy.
In a small bowl, whisk together the extra virgin olive oil and paprika. Pour the paprika oil into the pan and stir well.
Continue cooking for 30 more minutes, stirring every 5 minutes so the bottom does not burn. The matbucha should look glossy, thick, and deeply red.
Taste and adjust seasoning if needed. Let the matbucha cool slightly before serving warm, chilled, or at room temperature.