4 cups chicken stock
2 cups milk
1 ½ cups polenta or cornmeal
2 tbsp. fresh rosemary, coarsely chopped
4 tbsp. butter, cut into cubes
2 tsp. acacia honey
1 cup grated Parmigiano-Reggiano
1 cup dried porcini mushrooms
3 tbsp. EVOO
12 oz. cremini mushrooms, stemmed and sliced
½ lb. (2 heads) hen-of-the-woods or maitake mushrooms, trimmed and torn into pieces
1 large shallot, finely chopped
2 tbsp. fresh thyme, chopped, plus leaves for garnish
4 cloves garlic, thinly sliced
1 ½ tsp. coarse black pepper, plus more for garnish
½ cup Marsala wine
Heat chicken stock and milk in a large round-bottom pan, such as a risotto pot or Dutch oven, over low until barely simmering.
Whisk in the polenta until smooth, 2 to 3 minutes; season. Simmer, stirring occasionally, until thickened and creamy, 20 to 25 minutes. Stir in 3 tbsp. butter, the honey, and Parm.
In a small pot, combine porcini and 1 cup of water. Bring to a boil, then reduce heat to medium-low and simmer until softened, about 10 minutes. Remove and drain porcini, reserving ½ cup of cooking liquid. Once porcini are cool enough to handle, roughly chop.
In a large skillet, heat the EVOO, three turns of the pan, over medium-high. Melt the remaining 1 tbsp. butter into oil, then add the fresh mushrooms. Cook, stirring occasionally, until browned, 10 to 12 minutes. Add the shallot, thyme, garlic, and coarse black pepper; season with salt. Cook for a few minutes, until softened, then add the Marsala, porcini, and reserved porcini liquid. (Discard the last few tablespoons left in the pot as some grit may have settled in it.)
Ladle polenta into shallow bowls and top with mushrooms. Garnish with thyme leaves and pepper.