For the mushroom and cheese brioche: Cut the brioche into 1-inch cubes.
In a large bowl, whisk together the milk and eggs. Season with salt and pepper. Add the cubed brioche, truffle peelings, and chopped thyme to the bowl. Cover with plastic wrap and put in the refrigerator for 4 hours or overnight.
In a skillet over medium-high heat, saute the morels, button, and oyster mushrooms with the shallots for 2 minutes. Season with salt and pepper. Add 1/2 the Gruyere cheese to the brioche mixture, then add the mushroom- shallot mixture to brioche and cheese mixture.
Preheat the oven to 350 degrees F. Pour the bread pudding mixture in an oven-proof baking dish. Add the remaining cheese. Season with salt and pepper. Bake for 45 minutes or until puffed and golden brown.
For the poached eggs: Fill a saucepan with 3-inches cold water, add a pinch of salt and bring to a boil.
As the water reaches the boiling point, reduce the heat and allow the water to simmer.
Add 1 tablespoon vinegar to the water. Swirl the water around.
Break the eggs into a small plate or bowl and gently slide it into the water with care, holding the plate as near to the water as possible before allowing the egg to slowly slip into the water.
Once the eggs are in the water, you can help shape it using a spoon or spatula. Let the eggs cook for 3 to 3 1/2 minutes, allowing for the size of the egg and the preferred doneness of the egg yolks.
Remove each egg with a slotted spoon and drain for a few seconds on kitchen paper. Trim any stringy or dangling bits with a knife or scissors, if you wish.
Serve the poached egg on top of the truffle bread and garnish with a little bit of the microgreens dressed with olive oil and salt and pepper.
For your first attempt at preparing poached eggs, you may want to carefully break each egg onto a small cup, ramekin, plate or bowl before adding it to the water.
A perfectly poached egg has a lovely rounded shape, a soft yet firm white and a deliciously runny yolk. Time is of the essence when it comes to poaching eggs.
Problems will most definitely arise if the eggs are cooked at a temperature that is too high, if the eggs are not very fresh or if there is not enough water in the saucepan.
Use a saucepan or a deep frying pan, which allows you to fill it with about 3-inches of water. The eggs should be covered with water during cooking and the 3-inch depth of water ensures that the eggs will not stick to the pan.
Poached eggs must be cooked in water that is very gently bubbling or simmering. The water is first brought to the boil and then by turning the heat down on the cooker, is allowed to gently simmer. The eggs are carefully added to the pan at this point. If the water is boiling too fiercely, the eggs will be forced to move around too much, causing them to break up and lose their shape. A gentle simmer allows the egg to sit in one place throughout cooking and cook nicely.
By using the freshest eggs possible, eggs that are less than 4 days old, you are more likely to achieve a perfectly poached egg that keeps its shape. With a fresh egg, the white will stay close to the yolk and should not spread out thinly.
Vinegar should be added to the water as it begins to boil, as this will help the egg white to coagulate more quickly and form a neat and compact shape. Without the vinegar, disaster may occur. Use about 1 tablespoon vinegar for each pint of water. Bear in mind that the vinegar may slightly flavor the eggs, so do not use too much or a vinegar that is too strong, if you are not so keen on a vinegary tasting eggs.
For the more experienced cooks, break the egg above the pan and let it slip straight into the water.
Morels, oyster mushrooms, and button mushrooms can be replaced by any other mushroom.