In a 1 1/2-quart saucepan, add broth and dried porcini mushrooms. Bring mixture to boiling; reduce heat. Simmer, covered, for 5 minutes. Strain the broth through a fine mesh sieve and return to saucepan, reserving the mushrooms. Cover the broth and keep it simmering. Chop the mushrooms; set aside.
In a 3-quart saucepan, add butter, oil, onion, garlic, and fresh cremini mushrooms. Cook over medium heat for 3 to 5 minutes or until onion is tender, stirring occasionally. Add the rice; cook for 3 to 5 minutes or until rice is golden brown, stirring frequently.
Carefully stir 1/2 cup of the broth into the rice mixture. Cook over medium heat until liquid is absorbed, stirring frequently. Continue adding broth, 1/2 cup at a time, stirring frequently until the broth has been absorbed.
With the last addition of broth, add the porcini and cremini mushrooms. Stir until rice reaches a tender and creamy consistency. (This should take 20 to 25 minutes total.)
Stir in cheese; heat through. Sprinkle with thyme and serve immediately.