Prepare ingredients: measure polenta and milk, grate the Parmesan, thinly slice the mushrooms and pick thyme leaves. Prepping everything first keeps the timing tight and prevents overcooking the polenta or mushrooms.

Bring the milk to a gentle simmer: In a medium saucepan, combine 300 ml whole milk with a pinch (1/4 tsp) of salt and bring just to a simmer over medium heat. Warming the milk first prevents the polenta from clumping when added and yields a silkier texture.

Whisk in the polenta off the heat: Remove the pan from the heat and slowly whisk in 50 g instant polenta in a steady stream. Whisking while adding disperses the granules and prevents lumps. Return the pan to low heat.

Cook the polenta until creamy: Stir continuously for 2–3 minutes (instant polenta cooks quickly) until it thickens to a creamy, porridge-like consistency. Keep the heat low so it doesn’t stick — stirring disperses steam and avoids scorching. If it becomes too stiff, add 1–2 tablespoons warm milk or water to loosen.

Finish the polenta for shine and flavor: Remove from heat and stir in 20 g grated Parmesan, 1 tbsp unsalted butter (optional), and a generous pinch of black pepper. The cheese and butter enrich the polenta and give it a velvety mouthfeel; add seasoning now because dairy mutes salt, so taste and adjust.

Sauté the mushrooms: While the polenta cooks, heat 1 tbsp olive oil in a medium skillet over medium-high heat until shimmering. Add the sliced mushrooms in a single layer (crowding causes steaming), season with 1/4 tsp salt, and let them sit undisturbed 1–2 minutes to develop golden color. Turning them too early prevents browning; browning adds nutty, caramelized flavor.

Finish mushrooms with thyme and seasoning: Stir the mushrooms and cook another 2–3 minutes until tender and browned. Add 1 tsp fresh thyme leaves and a pinch of black pepper, toss for 30 seconds to release the thyme oils, then remove from heat. The fresh thyme brightens the earthy mushrooms and lifts the dish.

Set up for poaching: In a wide sauté pan bring 1 liter of water to a gentle simmer (small bubbles, not a rolling boil). Add 1 tsp white vinegar — this helps the egg whites coagulate quickly for neater poached eggs, but the flavor will be negligible in the finished dish.

Create a gentle whirlpool and poach the eggs: Using a spoon, stir the simmering water to create a gentle vortex, then crack one egg into a small bowl and slip it into the center of the whirlpool. Poach 3 minutes for a set white and runny yolk, or 3.5–4 minutes for slightly thicker yolks. The vortex helps the white wrap the yolk for a compact shape; keep the water just below a boil to avoid shredding the whites.

Remove and drain the eggs: Use a slotted spoon to lift each egg, gently pat the underside on a paper towel to remove excess water, and keep warm on a plate. If making two at once, poach them one after the other or use a wider pot to give each egg room.

Assemble the plates: Spoon half the creamy polenta into each shallow bowl, creating a slight well in the center. Nestle the soft-poached egg on top, then spoon the thyme-sautéed mushrooms around and over the egg. The polenta acts as a warm, creamy canvas that catches the yolk and mushroom juices.

Finish and season: Sprinkle each serving with the remaining pinch of salt (to taste), freshly ground black pepper, and an extra grating of Parmesan if desired. Drizzle a little olive oil or a small pat of butter for gloss. The finishing salt and fat enhance texture and flavor contrast.