In a large saute pan over medium-high heat, melt the butter. Add the onion, celery and carrots and cook until softened and the onion is translucent, about 8 to 10 minutes.
Add the flour and stir to coat. Stir in the milk, then the broth. Stir continuously and bring up to a simmer, cooking for 5 minutes. Remove from the heat and stir in the Monterey jack cheese. Season with salt and pepper. Stir the torn bread into the mixture, then spoon into the prepared baking dish, arranging it in an even layer. Sprinkle with Parmesan cheese, then bake for 25 to 30 minutes, or until bubbly and golden.
Nutrition information per serving: 340 calories; 150 calories from fat 44 percent of total calories); 17 g fat (9 g saturated; 0 g trans fats); 65 mg cholesterol; 33 g carbohydrate; 2 g fiber; 5 g sugar; 15 g protein; 590 mg sodium.