Squeeze out the soaked porcini and slice them into pieces about 1/4-inch wide. Strain the soaking water and keep it in a warm spot.
Clean, trim and slice the fresh mushrooms into moderately thin slices, about 1/4-inch wide.
Tie all the fresh herb sprigs together with piece of kitchen twine or enclose the leaves in cheesecloth.
Put the oil in the big skillet and place over medium heat. Then dump in the onions and shallots and 1/4 teaspoon of salt and stir well. Heat the onions to a slow sizzle and cook for 6 minutes or more-stirring often-until they’re soft, wilted and shiny, without any browning.
Pour all the mushrooms into the pan-both the chopped porcini and sliced mushrooms-spread and toss them in the pan. Sprinkle another 1/4 teaspoon salt, drop in the herb bouquet, toss briefly, raise the heat a bit and cover the pan. Cook covered for about 3 minutes-shake the pan now and then- to sweat the mushrooms.
Uncover and continue to cook over fairly high heat, stirring frequently, as the mushrooms shrink and the liquid evaporates, 5 minutes or more. When the pan is dry and the mushrooms begin to brown, clear a hot spot, drop in the tomato paste and toast it, stirring, for a minute or so, then stir it into the mushrooms.
When everything is sizzling and browning again, and just starting to stick, pour the balsamic vinegar stir until evaporated then add wine all over. Stir constantly as the wine thickens and evaporates. When the mushrooms again start sticking to the bottom, pour in the warm mushroom water and 2 cups of the hot stock. Bring to an active boil, stirring up any caramelization on the pan bottom. Lower the heat to keep the sauce bubbling gently all over the surface and cover the pan. Cook for about 20 minutes, occasionally stirring and adding stock to keep the mushrooms nearly covered in liquid; expect to add 1/2 cup or so. Adjust the heat to keep the perking steady but not too rapid.
Uncover the pan and cook for another 20 minutes, maintaining the simmer and adding stock as needed. When mushrooms are thoroughly tender and the saucy liquid thickened-but not too condensed-the sauce is done. Remove the herb bouquet and discard it (after you scrape off all the good sauce). Taste and add salt, if needed, and freshly ground black pepper to taste.
Use the sauce immediately over a bed of fried polenta with grilled lemon.
You can make a double batch let it cool. Then store it in the freeze, for later use within several months.