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1
Heat the broiler to low and arrange a rack in the upper third of the oven.
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2
Line a baking sheet with aluminum foil; set aside.
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3
Place russet and sweet potatoes in a large pot of heavily salted water and bring to a boil over high heat.
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4
Simmer until just tender when pierced with a knife, about 5 minutes.
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5
Drain, then return potatoes to the pot.
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6
Mash coarsely; add yogurt, salt, and pepper; and stir until just combined.
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7
Set aside.
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8
Heat olive oil in a large frying pan over medium heat until shimmering.
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9
Add mushrooms and cook, stirring rarely, until browned, about 6 minutes.
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10
Add onion, season with salt and freshly ground black pepper, and cook, stirring occasionally, until onion just begins to soften, about 3 minutes.
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11
Add carrots, celery root, tomato paste, and thyme and stir to coat vegetables.
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12
Add mushroom broth and soy sauce and stir until incorporated.
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13
Bring to a simmer, stirring occasionally, and cook until vegetables are just tender when pierced with a knife, about 10 minutes.
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14
Meanwhile, combine water and flour in a small bowl and stir until smooth.
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15
When vegetables are ready, add flour mixture, stir to combine, bring to a boil, and cook until sauce has thickened, about 1 minute.
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16
Season to taste with salt and freshly ground black pepper.
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17
Stir in frozen peas.
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18
Transfer mixture to a 7-by-11-inch baking dish (or a 3-quart baking dish) and spread reserved mashed potato mixture over top.
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19
Place on the prepared baking sheet and broil until the top starts to brown, about 5 minutes.
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20
Let cool 5 to 10 minutes before serving.
