Whisk all of the ingredients for the sauce together in a small bowl. Set aside.
To Cook the Mushrooms:
Heat the oil in a large skillet over medium-high heat. Add the mushrooms and cook until the liquid is released and then evaporated, about 5 minutes, stirring often.
Stir in 1 tablespoon of the prepared sauce and cook about 1 minute more, until absorbed. Transfer the mushrooms to a bowl and wipe out the pan.
To Fry the Eggs:
Heat the oil over medium heat in the same skillet you cooked the mushrooms in.
Once the oil is heated, crack the eggs into the pan. (There should be room for all 4 if your skillet is large enough; if not, cook them in batches.) Let the eggs cook until set, then remove from heat. (You can flip the eggs and cook them on both sides if you're not a runny yolk fan!)
To Assemble the Bowls:
Divide the rice into 4 bowls.
Top the rice with sweet potato slices, mushrooms, and one egg. Let everyone add the remaining ingredients to their liking; serve with sauce.
Notes
Roast the sweet potato at 400°F for 40–60 minutes, until tender.
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