To reconstitute the porcini mushrooms: Soak the mushrooms in 1 ½ cups of warm broth for about 30 minutes. Remove the mushrooms with a slotted spoon and set aside. Pour the liquid through a coffee filter, reserving flavorful liquid. Gently rinse the mushrooms under cold water and pat dry. I used the reserved liquid for the quinoa but you may add it to any recipe to achieve an intense mushroom flavor.
In a heavy 12-inch skillet, melt 3 Tbs. of the butter over medium-high heat. Add the mushrooms and cook, stirring only occasionally, until well browned, 5 to 7 minutes.
Add the garlic and cook, stirring, until golden and fragrant, about 45 seconds.
Add the vermouth, 3 Tbs. of the parsley or the white lower part of the green onions, the vinegar, salt, and pepper and boil until the liquid is reduced by half, about 2 minutes.
Remove the pan from the heat, add the seasoned cod to the pan ( tuck under the tails if necessary to even out the thickness), scrunch the fillets into the mushrooms then spoon some of the mushrooms and sauce on top.
Bring the mixture to a gentle simmer over medium heat, cover the pan, reduce to medium low, and simmer until just cooked through. Use a pairing knife to check the inside of the fish -- it should just not look raw. This should take about 7 to 12 minutes, depending on the thickness.
With a slotted spatula, transfer the fish to a serving platter.
Over low heat, whisk the remaining 1 Tbs. butter into the sauce. Spoon the sauce over the dish and serve sprinkling the remaining ½ Tbs. parsley or the green onions over it.