Let the dried porcini soak in hot water for at least 30 minutes until soft and pliable. Carefully remove the rehydrated mushroom from the soaking liquid being careful not to disturb the water too much. Squeeze the mushrooms in your hand to remove as much liquid as you can, allowing it to drip back into the jug. You want to save the mushroom liquid which is very flavorful. We'll add it back later. You should have about 1 cup (240ml) of soaking liquid left in the jug.
Coarsely chop the porcini mushrooms and set them aside with the stemmed and sliced shiitake mushrooms,
Heat the chicken stock in a medium pot and lower the heat to maintain a gentle simmer. If you are using store bought chicken stock there is generally no need to add extra salt to the pasta since the stock has plenty of salt already, but taste it to be sure. If it needs more seasoning go ahead and add it now. For homemade stock, season it with salt to your taste. *See note below
In a large pot heat 1/4 cup (110ml) of olive oil over medium heat. When the oil begins to shimmer add the penne, stirring constantly to agitate the pasta. Keep stirring until the pasta begins to color and become golden brown all over. This will take several minutes. Note that not all of the pasta will be evenly brown but all of them should have some color.
Carefully pour in the brandy or rum. (No need to use the good stuff here, it's just for flavor). The alcohol will erupt in a cloud of steam so keep you face away from the pot. Let the alcohol reduce, stirring all the time. This will only take about 20-30 seconds.
Add the hot chicken stock which should boil right away. Give the pot one last stir, lower the heat and partially cover the pot to maintain a gentle boil.
While the pasta cooks, heat the remaining 2 TBS (30ml) of olive oil in a 10" frying pan over medium high heat. Add the shiitake and porcini mushrooms and a generous pinch of salt. Reduce the heat to medium and cook the mushrooms, stirring occasionally until tender and the shiitakes begin to release their liquid, about 5 minutes.
Pour in the reserved mushroom soaking liquid, being careful not to get any of the residue at the bottom of the jug into the pan. **See note below. Add in the cream and give the pot a quick stir to combine the liquids and mushrooms. Bring to a boil then lower the heat to medium and let the liquid reduce and thicken slightly, stirring occasionally, about 8-10 minutes
Check on the pasta. It should be almost done by now but with still some stock left in the pot. Add the mushrooms and cream, stir and continue cooking, uncovered, until the pasta is done. Bite one to see. It won't be as soft and tender as boiled pasta because of the toasting process but there shouldn't be any raw pasta at its center. Once the pasta is cooked it should be quite soupy with some liquid left in the pot. That's as it should be: when you add the cheese it will emulsify the starchy, mushroom/cream and create a luscious sauce.
Remove the pot from the heat and let the pasta cool slightly, stirring occasionally to even out the temperature, about 5 minutes. Stir in the cheese and freshly ground pepper to your taste. Stir until the cheese melts and the sauce becomes creamy. If you add the cheese too soon when the pot is very hot it will tend to toughen up and become stringy rather than creamy. Feel free to add more cheese if you like (I usually like...). If you have any on hand you can throw in a handful of chopped parsley for a splash of color and fresh green flavor. Not essential but a nice touch at the end.
Serve on warm plates and enjoy with extra cheese sprinkled on top.