Heat oven to 350 degrees. If you have a Dutch oven or braiser that can go from stove to oven, start in this on the stove. If not, start with a wide, deep saute pan and transfer the mixture to a 3-quart (or 9×13-inch) casserole or baking dish for the oven part.

Heat 4 tablespoons olive oil over medium heat and add onion; cook 3 minutes, until softened. Add garlic and cook 2 minutes more. Add the carrots, 1 teaspoon salt, freshly ground black pepper, and red pepper flakes and cook for 2 more minutes, until they begin to glisten. Add the mushrooms and cook for 4 minutes, until they begin to soften. Add tomato paste and brown sugar and cook until well-incorporated, 3 minutes. Add 3 cups stock, vinegar, Worcestershire or soy sauce, chickpeas, and bay leaf and bring to a simmer with another teaspoon of kosher salt and more ground pepper.

Once simmering, either cover tightly with a lid or pour into your baking dish and cover with a lid or tightly with foil and transfer to oven. Braise chickpeas and vegetables for 90 minutes, checking at the 1 hour mark to make sure the chickpeas haven’t absorbed all of the broth (and adding the remaining 1 cup broth if so). Remove from oven, discard bay leaf, and adjust seasonings to taste.

Do ahead: Braised chickpeas will keep in the fridge for 4 days, and for a month or longer in the freezer. Reheat at 350 degrees.