Heat a large, heavy skillet over medium flame. Film the bottom with olive oil. Toss meat in seasoned flour. Brown the meat in the hot oil, a few pieces at a time (do not crowd the pan or the meat will simmer instead of brown). As pieces are browned, transfer them to a heavy pot. If necessary, add a bit more oil to the skillet with each batch.

When all the meat is browned, add a bit more oil to skillet and add the chopped onions. Cook, stirring often, until they begin to soften. Transfer onions to the pot with meat. Stir beer, tomato paste, thyme, and oregano into the skillet; bring to simmer, stirring to scrape up any bits on the bottom. Pour beer mixture into pot with meat and onions. Bring to simmer, lower heat, cover, and cook very slowly.

As stew begins to cook, pour 1 cup boiling water over dried mushrooms. Let stand until mushrooms are soft, about 5 minutes. Strain the mushroom liquid through cheesecloth or a thick layer of paper towels into a bowl. Remove soaked mushrooms from the cheesecloth, rinse them, and add them to the stew. Now stir the strained liquid and both kinds of fresh mushrooms into stew. (Don't worry if it seems as if there's not enough liquid; the mushrooms will throw off additional liquid as they cook.)

Return stew to very slow simmer, partially cover it, and continue cooking, stirring occasionally, until meat is very tender and stew is thickened, 1-2 hours. (Alternatively, stew may be cooked in 300-degree oven.) Season to taste with salt and pepper. Although the stew will be rich and flavorful at this point, it will be incredible if you make it a day ahead and reheat before serving.