I loved polenta from the moment I first tasted it in Italy, but never so much as since adopting a gluten-free diet. Here it is a creamy base for mushrooms simmered with shallots, thyme, and wine, and tender poached eggs.
In a large nonstick frying pan over medium-high heat, warm the oil. Add the cremini and shiitake mushrooms and sprinkle with salt and pepper. Sauté until starting to soften, about 3 minutes. Add 3 tablespoons of the shallots and the 1 tablespoon thyme and sauté for 2 minutes. Add the wine and tomato paste and simmer until the liquid becomes syrupy, 1–2 minutes. Adjust the seasoning. Cover and keep warm.
Prepare the polenta, adding the remaining shallots to the bowl before cooking. While the polenta cooks, poach the eggs.
Divide the polenta between 2 warmed plates, spreading in a circle. Spoon the mushrooms over the polenta. Using a slotted spoon, remove the eggs from the poaching water one at a time, drain off any water, and set atop the mushrooms. Sprinkle the eggs with thyme and pepper and serve right away.