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Preheat oven to 350 degrees F.
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In large skillet over medium heat, add olive oil. Add chopped onion and cook until softened, about 5 minutes. Add minced garlic and cook another minute until fragrant.
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Add trimmed green beans and sliced mushrooms to skillet. Cook, stirring occasionally, until green beans are tender-crisp and mushrooms are softened, about 8-10 minutes.
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Sprinkle all-purpose flour over green bean mixture and stir well to coat everything evenly. Cook 1 minute, stirring constantly.
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Gradually pour in vegetable broth and plant-based milk, stirring constantly to prevent lumps from forming. Bring mixture to simmer and cook until sauce has thickened, about 3-5 minutes.
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Stir in soy sauce, salt, black pepper and nutritional yeast. Taste and adjust seasonings as needed.
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Remove skillet from heat and stir in 1/2 cup vegan fried onions, reserving remaining 1/4 cup for topping.
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Place phyllo dough cups on a baking sheet.
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Spoon green bean mixture into phyllo dough cups, filling each cup to the top.
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Sprinkle remaining 1/4 cup vegan fried onions over top of the filled phyllo cups.
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Bake in preheated oven 10-15 minutes, or until the phyllo cups are golden brown and filling is heated through.
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Remove from oven and let cool a few minutes before serving.