In a small bowl, dissolve the cornstarch in the water. Set aside.
In a saucepan, melt the butter. Add the flour and continue cooking for about 5 minutes, stirring constantly, until the mixture (the roux) turns golden brown. Stir in the garlic and continue cooking for 30 seconds.
Add the beef and chicken broths and bring to a boil while stirring with a whisk. Stir in the dissolved cornstarch mixture and simmer for 3 to 5 minutes or until the gravy thickens. Season with the cayenne pepper.
With two racks in the middle positions, preheat the oven to 450°F (230°C). Line two baking sheets with silicone mats or parchment paper.
On a work surface, cut all of the vegetables, except the beans, into 1/2-inch (1 cm) thick sticks. Spread the russet or Yukon Gold potatoes, carrots and parsnips on a baking sheet. Toss to coat with 2 tbsp (30 ml) of the olive oil and season with salt and pepper. Bake for 15 minutes. Remove from the oven and turn the vegetables.
Meanwhile, on the second baking sheet, spread the sweet potatoes and green beans. Drizzle with the remaining oil (1 tbsp/15 ml) and season with salt and pepper. Bake both sheets of vegetables for 15 minutes or until the vegetables are tender and lightly browned.
Transfer the vegetables to shallow serving plates. Sprinkle the cheeses over the vegetables. Drizzle with the warm gravy. If needed, return to the oven for about 3 minutes to melt the cheeses.
This recipe contains 12 servings of vegetables (not counting the potatoes!).
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.