In large saucepan, bring water and salt to a boil. Add corn meal gradually, whisking continually. Once you have added all the cornmeal, lower the heat, cover and simmer for about 20-25 minutes, until the polenta has reached desired consistency. Add more water if needed.
Take off heat, stir in fresh thyme and pepper. Cover and set aside until plating.
Drizzle a little bit of olive oil in a medium non stick frying pan and heat over medium-high heat. Add oyster mushrooms and cook until nice and golden on both sides, about 1 minute per side.
Meanwhile, poach the egg by first cracking the egg into a small bowl and setting it aside. Then, heat a good amount of water in a shallow pan, add a pinch of salt and about a teaspoon of lemon juice. When water starts to simmer, gently slip the egg in the water and push it back with a spoon to help it take its shape. Cover and cook for about 2-3 minutes, until white is completely set and opaque but yolk is still runny. Remove from water and pat dry on a paper towel.
Laddle polenta onto shallow serving plate. Top with oyster mushrooms and poached egg. Sprinkle blue cheese and chopped pistachios on top. Garnish with a few sprigs of fresh thyme.