Pappardelle with Vegetable "Bolognese"

I adapted this recipe from one I found on epicurious.com. I think my version is a little heartier!

2 medium carrots, quartered lengthwise, then cut into 1-inch pieces
2 celery ribs, cut into 1-inch pieces
3 medium shallots, quartered lengthwise
1 medium red bell pepper, cut into 1-inch pieces
package of baby portobello mushrooms
3 tablespoons olive oil
2 teaspoons chopped fresh rosemary
3/4 teaspoon salt
1/2 teaspoon black pepper
2 tablespoons tomato paste
1/2 cup dry red wine
1-2 cups chicken or vegetable stock
3/4 lb dried pappardelle
1 oz finely grated Parmigiano-Reggiano (1/2 cup) plus additional for serving

Pulse carrots, celery, shallots, bell pepper and mushrooms together in a food processor until chopped.

Heat oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking. Add chopped vegetables, rosemary, salt, and pepper and sauté, stirring occasionally, until vegetables are golden brown and tender, about 12 minutes.

Add tomato paste to skillet. Cook over moderate heat, stirring, 1 minute. Add wine and boil until wine is reduced by about half, about 2 minutes.

While sauce is cooking, cook pasta in a 6- to 8-quart pot of boiling salted water until al dente. Reserve 1 cup pasta-cooking water in a heatproof measuring cup, then drain pasta in a colander.

Add chicken stock to sauce and bring to a simmer. Add pasta and 1/2 cup reserved cooking water to sauce, tossing to coat (thin sauce with additional cooking water if necessary). Stir in cheese and serve immediately.