Place frozen rice cakes in a large bowl and soak them in cold water to thaw for about 20 minutes. Set aside.
Combine the heavy cream and milk together and set aside.
In a large skillet over medium high heat, add the olive oil and stir-fry the garlic, followed by the onion, until fragrant and onion becomes slightly translucent. Add in the bacon/ham and continue to stir-fry. Then add in the mushrooms and rice cakes and mix together.
Pour in the heavy cream & milk mixture and keep stirring when it starts to boil (so that the rice cakes don’t stick to the bottom). Continue to stir the mixture until the rice cakes turn soft.
Add in the broccoli and cook for a few minutes. Season with salt, pepper, garlic powder and oregano. Mix well. Remove from the heat and add in the parmigiano reggiano (or parmesan) and combine everything well together. Serve and enjoy!