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1
In a large saucepan over medium-high heat, warm 2 tablespoons of the oil.
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2
Add the yellow onion, sprinkle with salt, and sear, without stirring, until browned, about 5 minutes.
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3
Stir in the leek, garlic, ginger, dried mushrooms, and 6 cups water and deglaze the pan, stirring and scraping up any browned bits from the bottom.
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4
Reduce the heat to medium-low, partially cover the pan and simmer until fragrant, about 1 hour.
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5
Strain the broth through a fine-mesh sieve into a bowl and discard the solids.
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6
Meanwhile, preheat the oven to 400 degrees F. Add the sweet potatoes to a baking sheet and drizzle with a little oil; toss and spread into an even layer.
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7
Cut the top quarter of the head of garlic off and discard.
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8
Drizzle the cut side of the garlic head with a little oil and wrap with foil.
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9
Add to the sheet pan.
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10
Roast, stirring the potatoes occasionally, until tender and tinged with brown, and the garlic is very tender.
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11
Remove from the oven.
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12
Squeeze the garlic cloves into a blender and add 1/3 cup of the roasted sweet potatoes with 1/2 cup broth.
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13
Puree until smooth and add to the broth.
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14
In the saucepan over medium heat, add the remaining 1 tablespoon of oil.
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15
Add the mushrooms and cook, stirring, until tender.
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16
Add the broth and season to taste with soy sauce.
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17
Bring to a simmer, then reduce the heat to low, cover partially, and simmer until warmed through.
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18
Whisk in the miso.
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19
Divide the noodles evenly among individual bowls.
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20
Ladle the broth over the noodles, dividing them evenly, then top with the roasted sweet potatoes.
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21
Sprinkle with the green onions and serve.
