Fried Cauliflower with Roasted Red Pepper-Walnut Sauce

Roasted Red Pepper–Walnut Sauce: Pulse bread and walnuts in a food processor until fine crumbs form. Add remaining sauce ingredients; process until sauce is emulsified and thick. Fried Cauliflower: Bring a large pot of lightly salted water to a boil; cook cauliflower until almost tender, about 5 minutes. Drain; cool under cold water. Whisk eggs, cheese, and cayenne in a small bowl; spread breadcrumbs on waxed paper. Dip cauliflower in egg mixture then in breadcrumbs to coat; transfer to a wire rack. Spread capers on a paper towel; let cauliflower and capers air-dry 10 minutes. Heat 1/4 cup of the oil in a large nonstick skillet over medium heat, until hot. Add capers; fry 1 to 2 minutes, until crisp. Remove from skillet with a slotted spoon; drain on paper towel. Add remaining 1 cup oil to skillet and heat over medium heat until hot but not smoking. Fry cauliflower, a few pieces at a time, 4 minutes, turning with tongs until golden brown and crisp; drain on paper towel. Transfer to a serving plate and scatter with fried capers. Serve with Roasted Red Pepper–Walnut Sauce and lemon wedges.