In a medium saucepan, bring chicken stock to a boil. Add sage, 1/2 teaspoon pepper, 1/2 tablespoon garlic and both rices. Cover, lower to a simmer, and cook for 40-50 minutes, stirring periodically to check that you still have water.
You want your rice to just be tender. Test it at 40 minutes. If it gets over cooked, it will be mush once you bake it.
Meanwhile, heat olive oil in a large skillet over medium-high heat and preheat your oven to 400 degrees.
Add onion, carrots, celery, salt, and remaining 1/2 teaspoon pepper and 1/2 tablespoon garlic. Cook over medium heat for 5 minutes.
Add broccoli and cook an additional 5 minutes, until vegetables have just become tender.
Stir in cooked rice. Taste and add salt and pepper, if needed.
Pour rice/vegetable mixture into a greased casserole dish and bake in the oven for 15-20 minutes, until the rice just begins to crisp up on the top. Serve.