Choose miso depending on how assertive you like the flavor: White is mildest, red is strong and yellow tastes somewhere between the two. Be sure not to overcook the noodles.
On cutting board, mince 1 clove garlic, then mash into paste using flat side of knife; set aside. Crush remaining clove garlic and set aside.
In large saucepan, whisk together miso and 6 cups water until miso dissolves. Add garlic paste and mushrooms and bring to a boil over high heat, stirring occasionally. Reduce heat to low, cover and simmer until mushrooms are tender, 5 to 6 minutes.
Uncover pan, increase heat to high and return to a boil. Add noodles; stir to separate. Cover, reduce heat to low and simmer until noodles are just barely tender, about 5 minutes. Turn off heat; do not remove cover.
While noodles are cooking, in large skillet, heat oil over medium heat. Add crushed garlic and cook, turning often, until browned, about 3 minutes. Discard garlic. Increase heat to medium-high, add mixed vegetables and cook, stirring, until tender and beginning to brown, 7 to 10 minutes. Remove from heat.
Divide noodles, mushrooms and broth among 8 heated shallow serving bowls. Top each with some vegetables and serve hot.