Broccoli Barley Soup

Ingredients

• medium onions, chopped (2)
• garlic cloves, minced (2)
• sliced fresh mushrooms (4 ounces)
• butter (3 tablespoons)
• chicken broth (3 cups)
• vegetable broth (3 cups)
• uncooked medium pearl barley (3/4 cup)
• dried rosemary, crushed (1/4 to 1/2 teaspoon)
• fresh broccoli, cut into florets (1 pound)
• cornstarch (2 tablespoons)
• cold water (1/4 cup)
• half-and-half cream (2 cups)
• Grated Parmesan cheese