How to Make It
Preheat broiler to high.
Cut bell peppers in half lengthwise; discard seeds and membranes. Place halves, skin sides up, on a foil-lined baking sheet; flatten with hand. Broil 10 minutes or until blackened. Wrap peppers in foil; let stand 10 minutes. Peel; cut into thin strips.
Combine vinegar, brown sugar, salt, and pepper in a medium bowl, stirring with a whisk. Set aside.
Heat oil in a high-sided sauté pan over medium-high heat. Add onion; cook 3 minutes or until softened. Add cauliflower and mushrooms; cook 3 minutes or just until lightly browned, stirring frequently. Add roasted peppers, garlic, and thyme; cook 2 minutes, stirring constantly. Pour vinegar mixture over vegetables. Cover, reduce heat to low, and simmer 8 minutes or until cauliflower is tender, stirring occasionally. Transfer escabèche to a bowl; cool completely. Cover and chill 24 hours or up to 1 week. To serve, let vegetables come to room temperature, and remove from brine using a slotted spoon.