6 large portobello mushroom caps, gills scraped with a spoon and caps cut into 1/4-inch-thick slices
⅓ to 1/2 cup olive oil
4 cloves garlic, thinly sliced or crushed
2 tbsp. fresh rosemary, chopped
1 ½ tsp. (about 1/2 palmful) crushed red pepper
1 ½ tsp. (about 1/2 palmful) ground cumin
1 tsp. (about 1/3 palmful) dried thyme, lightly crushed
½ tsp. ground allspice
Salt and coarsely ground black pepper
About 2 cups grated Parmigiano-Reggiano (for an entrée)
4 large eggs (for an entrée)
4 cups chicken or vegetable stock
About 1 1/3 cups quick-cooking polenta
3 tbsp. butter, cut into 3 pats
1 rounded tbsp. acacia honey or other mild honey (optional)
Chopped fresh chives
Arrange a rack in the center of the oven; preheat to 450°. Line a large baking sheet with parchment paper.
In a large bowl, toss the mushrooms, oil, garlic, rosemary, crushed red pepper, cumin, dried thyme, allspice, and a generous amount of salt and coarsely ground pepper. Arrange the mushrooms on the baking sheet in an even layer. Roast for 10 minutes. Turn the mushrooms over and roast until browned, 10 to 12 minutes more.
If serving as an entrée, for the frico, heat a small (6-inch) nonstick skillet over medium. (If you have 2 skillets, you can make 2 frico at a time). Evenly scatter 1/4 to 1/3 cup cheese in the skillet. When it begins to bubble (1 to 2 minutes), crack an egg on top. Cover with a lid or foil. Cook until the white is set, about 2 minutes. Transfer to a plate. Repeat with the remaining cheese and eggs.
Meanwhile, in a medium saucepan, heat the stock over medium. When the mushrooms are about ready, add the polenta to the stock and whisk until thick, 2 to 3 minutes. Remove from heat. Add the butter and whisk until melted. Add any remaining cheese and the honey (if using). Season with salt and pepper. (If the polenta gets too thick, whisk in enough stock to make it spoonable.)
For a starter, swirl the polenta on small plates to create a well; fill with the mushrooms. Top with chives. For an entrée, serve the polenta and mushrooms topped with frico eggs and chives.