In small bowl, soak dried mushrooms in 3/4 cup boiling water 30 minutes.
Meanwhile, cut off and discard stems from shiitake mushrooms; trim stem ends from white mushrooms.
Wipe both kinds of mushrooms to remove any sand.
With slotted spoon, remove porcini mushrooms from soaking liquid, reserving liquid.
Rinse porcini mushrooms to remove sand; chop.
Strain soaking liquid through sieve lined with paper towel.
Set aside.
In 8 quart Dutch oven, heat vegetable oil over medium high heat.
Add brisket and brown on both sides, about 10 minutes.
Remove brisket and set aside.
Add onions to Dutch oven and cook over medium heat until they are lightly browned, about 15 minutes, stirring occasionally.
Stir in garlic slices and cook 30 seconds.
Stir in flour and cook until browned, about 2 minutes.
Preheat oven to 325°F.
Return brisket to Dutch oven.
Stir in chopped porcini mushrooms, mushroom liquid, whole shiitake and white mushrooms, broth, red wine, brandy, sage, bay leaf, thyme leaves, salt, pepper, and 2 tablespoons chopped parsley.
Heat to boiling over high heat.
Cover; place in oven and cook 2 1/2 hours or until brisket is fork tender.
Remove meat from Dutch oven to large platter; let stand 15 minutes.
Skim fat from sauce in Dutch oven.
Discard sage and bay leaf.
Heat sauce to boiling over high heat.
Reduce heat to medium high and cook, uncovered, 15 minutes to thicken sauce slightly.
Stir remaining 2 tablespoons parsley into sauce.
Slice brisket across the grain.