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1
Turn oven to broil and line a rimmed baking sheet with parchment paper.
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2
Place the peppers on the baking sheet and broil, turning over every 30 seconds, until skins are blackened in spots. Place the peppers in a large bowl and cover tightly with plastic wrap for 10 minutes. Peel the peppers' skins with your fingers.
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3
Cut the peppers, removing the white ribs and seeds; then rinse and pat dry. Place the peppers, garlic, oil, hazelnuts, tahini, vinegar, paprika, salt, and cayenne (if using) in a food processor. Blend until smooth and creamy. Transfer the sauce to a bowl and cover with plastic wrap until ready to use. (Rinse food processor and set aside.)
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4
Cook the quinoa with 1 cup of water for 12 to 14 minutes, until cooked and water has evaporated; set aside. Meanwhile, fill a small saucepan three-quarters of the way with water, add the mung beans and bring to a boil, turn heat down to a simmer and cook for 25 to 30 minutes, until tender and doubled in size; drain any remaining water and set aside.
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5
In a small bowl, whisk together the flaxseed and 3 tablespoons of water; let mixture sit for 10 minutes, until thick.
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6
In the food processor, add the cooked quinoa, mung beans, flaxseed mixture, parsley, flour, shallots, garlic, lemon juice, salt, and spices. Blend until thoroughly combined; taste for salt and lemon and adjust if necessary. Transfer to a large bowl and stir in the sesame seeds; cover with plastic wrap and refrigerate for 1 hour or overnight.
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7
Preheat oven to 375u00b0 F (190u00b0 C) and line two baking sheets with parchment paper; set aside.
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8
Pinch off golf ball-size pieces of mixture and roll between palms to shape into a ball. Place on prepared baking sheets and repeat.
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9
Lightly brush the tops and bottoms of the falafel with oil. Bake for 20 to 25 minutes, rotating the baking sheets and flipping falafels over halfway through the baking time.
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10
Serve warm with romesco sauce and garnish with parsley.
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11
*To toast the chickpea flour. Place 1 cup of chickpea flour in a large skillet, turn the heat to medium, and stir. Keep stirring for 5 to 7 minutes, until the flour is lightly browned and has a nutty fragrance. Place in a bowl or on a plate and let it cool at room temperature. Store toasted chickpea flour in an airtight container at room temperature if not using right away.