Heat 2 tablespoons vegetable oil in 12-inch skillet over medium heat until shimmering. Add red pepper, carrots and onion, and cook, stirring occasionally, until vegetables are browned and soft, about 10 minutes. Season with salt and pepper. Add garlic and cook, stirring constantly, until aromatic, about 30 seconds.
Transfer vegetables to medium bowl. Add quinoa, egg, scallions, lemon juice and 2 teaspoons matzah meal. Stir until combined.
Using ¼-cup measure, scoop out 10 cakes and form them into 2.5- to 3-inch patties. Place on sheet pan and refrigerate for 30 minutes. Meanwhile, spread matzah meal in shallow dinner plate and season with ½ teaspoon salt and ¼ teaspoon pepper. Whisk to combine.
After 30 minutes, heat ¼ cup vegetable oil in 12-inch skillet over medium heat until shimmering. Roll one patty in matzah meal until fully coated. Let excess fall back into plate. Repeat with remaining patties. Carefully place five patties in pan and cook until golden brown, about 5 minutes. Flip and cook until second side is golden brown, about 3 more minutes. Transfer to paper towel-lined plate. Repeat with remaining patties. Serve immediately.
Sauce Mix ¼ cup mayonnaise, 1 teaspoon Dijon mustard, 1 teaspoon lemon juice and 1 minced garlic clove.