In a large nonstick skillet, melt 1 tablespoon of the butter in 1 tablespoon of the olive oil over moderately high heat. Add the shiitake and cremini mushrooms, season with salt and pepper and cook, stirring, just until they exude their juices and begin to brown, about 3 minutes. Transfer the mushrooms and any of their juices to a bowl.
In a medium, shallow saucepan, heat the remaining 1 tablespoon each of butter and olive oil. Add the onion and garlic and cook over moderate heat until the onion begins to soften, about 3 minutes. In a large heatproof measuring cup, heat the stock in the microwave at full power for 2 minutes, until piping hot.
Add the rice to the onions and garlic and stir until coated with the oil and beginning to sizzle, about 2 minutes. Add the wine and stir until absorbed. Add 1/2 cup of the hot stock to the pan and cook, stirring constantly, until most of it has been absorbed by the rice, about 4 minutes. Continue to cook the risotto, adding the stock 1/2 cup at a time and stirring constantly between additions until it is absorbed; look for large bubbles on the surface of the rice before adding more stock. Stir in the cooked mushrooms and their juices with the last addition of stock. The risotto is done when the rice is al dente and suspended in a creamy sauce, about 25 minutes total.
Remove the risotto from the heat and stir in the Parmigiano and fontina. Season the risotto with salt and pepper and serve immediately.