Place dried mushrooms in a heatproof bowl and cover with boiling water. Let stand for at least one hour. Remove mushrooms and slice, discarding tough stems. Strain broth through a coffee filter and reserve.
Heat 2 tablespoons canola oil in a large skillet over medium-high heat. When hot, working in batches so the pan only contains a single layer of mushrooms, sear mushrooms, without stirring, for 2-3 minutes. Stir and sear the other side of the mushrooms. Season with salt and pepper, remove from pan and set aside.
Lower heat to medium low, add butter and flour and cook, stirring often, until browned, about 10 minutes.
Add onions and garlic, stir and cook until tender, about 5 minutes. Add wine, stirring to deglaze the pan and allowing everything to thicken. Add broth in two equal amounts, stirring to form a gravy. Season with thyme and vinegar. Taste and adjust seasoning with salt and pepper. Add mushrooms, and turn to low to keep warm.
Preheat oven to 400°F.
Bring a large kettle of salted water to a boil. Add carrots and cook until tender, about 4 minutes. Remove with slotted spoon and drain. Cook squash in the same way, boiling for about 2 minutes, remove with slotted spoon to drain. Cook potatoes for about 7 minutes, then drain. Finally, cook peas and beans until thawed, 1 to 2 minutes. Drain.
Put vegetables in a 9x13 inch pan, cover with gravy, and top with biscuit dough.
Bake 15 minutes, lower temperature to 325°F for 30 minutes. Finally, if biscuits aren't quite browned enough, broil for 1 to 2 minutes.