In a small mixing bowl, add the shiitake mushrooms, soy sauce, liquid smoke, maple syrup and paprika. Toss to coat the mushrooms.
In a large non-stick skillet or cast iron pan, heat the olive oil on medium high.
Add the shiitakes and sauté, reducing heat as needed until they are golden brown. About 7 to 9 minutes. Leave the pan on low to keep warm while you make the polenta.
In a medium sized sauce pan, whisk together 2 cups of non-dairy milk, the vegetable broth and the salt. Heat on medium high.
Bring to a simmer and then reduce heat to medium and very slowly stream the polenta into the sauce pan, whisking the entire time to make sure you don't get any lumps.
Reduce heat to medium low, cover and let simmer for 8 to 10 minutes or until the polenta is very thick and tender.
While the polenta simmers, in a small mixing bowl, whisk together the vegan egg and the remaining 1/4 cup of non-dairy milk.
Once the polenta is done, add the vegan butter, vegan parmesan and the vegan egg mixture to the sauce pan and whisk to combine, letting everything melt into the polenta and cook for 1 to 2 more minutes.
Serve immediately. Pour some of the polenta in a bowl, top with the shiitake mushroom "bacon", some extra Parmesan if desired. I recommend serving with roasted veggies or tofu!