Cut mushrooms in half or, if too large, into 4 pieces.
Heat a good splash of olive oil in a saute pan over high heat.
Toss the mushrooms in the hot oil. Season with 1 teaspoon dried thyme. Shake and toss until they get a brownish colour, about 2-3 minutes. Then transfer to a bowl and keep aside.
In the same pan, add another splash of olive oil. Enough to coat the bottom of the pan.
Add the onions and season with salt. Caramelize the onions over moderate heat for 15-20 minutes.
Pour in the balsamic and stir until it drains.
Add the brown sugar and stir to combine.
Pour in the wine and cook uncovered for 2-3 minutes until it stops smelling of alcohol.
Add the allspice, sprigs of thyme, crushed tomatoes, and garlic. Pour in the water or stock. Season with salt and pepper.
Cook over moderate heat, partly covered, until the sauce thickens. Raise the heat to high.
Add the mushrooms and cook on high for 4-5 minutes.
Serve with freshly ground pepper.