Homemade brown BBQ gravy - Le Coup de Grâce

Ingredients

• Olive oil
• 4 chicken wings
• 1 yellow onion, finely chopped
• 1 garlic clove, finely chopped
• 5 big white mushrooms, sliced
• 1 big carrot, cut lengthwise then sliced
• 1/4 teaspoon Italian spices
• 1/4 cup dark rum
• 8 cups low sodium chicken broth, hot
• 1/2 tablespoon tomato paste
• 1 bay leave
• 1/4 cup barbecue sauce
• 3 tablespoons corn starch diluted in 1/3 cup cold water
• Salt and ground pepper