In a large, heavy-bottomed sauté pan, add 2 tbsp vegetable oil and turn the heat to medium.
When the oil is hot, add the pork chops and brown on one side, then the other.
Add the white wine and simmer it for 15-20 seconds, scraping any browning residue from the bottom of the pan.
Add the tomatoes, cream, salt pepper, and the chopped reconstituted porcini mushrooms.
Turn the heat down to low and simmer, with the lid of the pan slightly ajar.
Cook for 45 minutes, turning the chops from time to time, until they are fork-tender.
While they cook, put the filtered water from the reconstituted porcini mushrooms in a small sauce pan and bring to a simmer. Boil it down to about ⅓ cup.
In another sauté pan, add the remaining 2 tbsp oil and turn the heat to medium.
When the oil is hot, add the sliced fresh mushrooms and stir frequently, adding salt and pepper.
When the liquid from the fresh mushrooms has boiled away, add the reduced porcini water and continue to stir until all of that liquid has boiled away. Remove from the heat.
When the pork chops are fork-tender, add the cooked mushrooms to the pan. Turn the chops a few times, cover, and continue cooking for another 5-8 minutes over medium-low heat.
Transfer everything to a warm platter and serve immediately.