Preheat oven to 400 degrees Fahrenheit.

Place eggplant, garlic, shallots, jalapeños, and cherry tomatoes (if using) on a baking sheet. Drizzle with 1/4 cup oil and season with half a teaspoon of salt, black pepper to taste, and half a tablespoon of paprika.

Roast 25 to 30 minutes.

While the vegetables roast, pour diced tomatoes into an oven-safe pot with remaining 1/3 cup oil, remaining half a teaspoon of salt, black pepper to taste, and remaining half a tablespoon of paprika.

Bring to a low boil. Reduce heat to a simmer and cook 30 minutes, covered.

Remove vegetables from the oven and reduce temperature to 325 degrees Fahrenheit.

Squeeze garlic cloves into the pot. Chop or mash the other roasted vegetables and add to the pot, stirring to combine.

Cover pot and cook in the oven for about one hour, until liquid evaporates, oil rises to the surface, and the color is a deeper red, almost burgundy (see note).