Soak porcini mushrooms in hot water for at least 30 minutes. Set aside, reserving the liquid.
In a medium saucepan, sauté shallots, garlic, and carrots in two tablespoons of butter over medium heat for about 5 minutes, until the shallots are lightly browned.
Stir in the tomato paste and cook for about 2 minutes.
Deglaze the pan with the wine, scraping the bits and pieces that have stuck to the pan. Stir in thyme, sugar, and porcini mushroom (with the liquid).
Bring to a boil over high heat, then lower the heat to a simmer, and cook until the liquid is reduced by half, about 15 minutes.
Remove from heat, add the reserved two tablespoons of butter and whisk until smooth.
Strain through a fine sieve into a saucer and keep warm until ready to serve.