Pour the balsamic vinegar and approx. 250 ml water into a saucepan. Add the sun-dried tomatoes and a generous pinch of sugar. Bring to a boil over medium-high heat.
Reduce to medium heat and simmer for 7-10 minutes until the tomatoes are soft but not falling apart. While simmering, finely chop the rosemary.
Drain the tomatoes through a sieve and collect the cooking liquid.
Transfer the drained tomatoes to a bowl, mix with the chopped rosemary, cool for a few minutes, then mince and stir in the 3 garlic cloves.
Pour 3-4 tablespoons of the cooking liquid over the mixture and stir.
Add the olive oil and mix well.
Refrigerate and let the tomatoes steep for at least 24 hours, preferably 48 hours before serving.