Combine water and porcini mushrooms in a small bowl, and let stand for 20 minutes.
Heat olive oil in a small saucepan over medium-high heat.
Add onion, cremini mushrooms, carrot, and garlic; saut 10 minutes or until onion is browned. Reduce heat to medium. Stir in wine, flour, marjoram, and tomato paste. Cover and cook for 3 minutes or until mixture is syrupy.
Add porcini mixture, vinegar, salt, and pepper; cook 20 minutes. Strain through a sieve into a bowl. Discard solids.