In a large saucepan over medium heat, heat the oil. Add mushrooms, onion, and garlic and cook until onion is tender.
Add rice. Cook and stir for about 5 minutes more until rice is golden brown.
Meanwhile, in another saucepan, bring broth to a boil; reduce heat and simmer. Slowly add 1 cup of the broth to the rice mixture, stirring constantly.
Continue to cook and stir over medium heat until the liquid is absorbed. Add another ½ cup broth and the asparagus to the rice mixture, stirring constantly. Continue to cook and stir until liquid is absorbed. Add another 1 cup broth,½ cup at a time, stirring constantly until the broth has been absorbed. (This should take about 15 minutes.)
Stir in the remaining ½ cup broth, tomato, and carrot. Cook and stir until rice is slightly creamy and just tender. Stir in basil. Serve immediately.
