Start the tomato jam by heating a medium sauce pot over medium heat. Add oil and onions and cook for a minute undisturbed, until some light browning occurs, then stir and continue cooking this way until the onions are almost fully browned. Add garlic, tomatoes, vinegar, sugar and salt and bring to a simmer. Cook, stirring occasionally, for roughly an hour, until there is no liquid left and the jam can hold its own when a line is drawn with a spoon on the bottom of the pot. Allow to cool until the dough is ready to roll.
Meanwhile, make the dough by melting the butter over medium low heat in a small pot. Once melted, turn off the heat and add milk. Pour milk and butter into the bowl of a stand mixer fitted with the dough hook, add the yeast and stir to combine for a few seconds then allow the yeast to bloom for a minute undisturbed.
Add the remaining ingredients and mix together for about 5 minutes, until the dough is pulling away from the sides of the bowl and a small trail forms on the bottom. Turn the dough into a lightly greased bowl, cover and let proof in a warm place for about an hour, until doubled in size.
When the first rise of the dough is done, roll it out on a clean, lightly floured surface, to a rectangle approximately 16 x 13 x ¼-inch thick. Spread the tomato jam evenly on the dough leaving about a 1 ½-inch border on one of the long edges, and a ½-inch border along the rest of the edges. Roll the dough towards the wide bordered edge leaving the seam on bottom and cut into 12 pieces.
Lightly grease a 13 x 9-inch baking pan and evenly space the slices cut side down in 4 rows of 3. Cover and allow the rolls to proof for another hour, or until doubled in size.
Heat the oven to 350°F, and bake the rolls for about 45 minutes, or until they are golden, with some light brown edges developing.