Heat the olive oil in a 12-inch skillet over medium-high heat until hot. Add garlic, don’t burn it. Add half of the mushrooms in a single layer and brown them on 1 side, 2 to 3 minutes. Add the remaining mushrooms, brown. Add fish sauce, stir and cook for a minute and add Worcestershire, cook for a minute and then stir butter in (save some butter for the toast). Turn off heat. Add parsley and mix in. Keep aside until ready.

Slice radishes paper thin on a mandoline. Watch your fingers! Bring 3 quarts of water, the vinegar and ½ tablespoon salt to a boil in a 4-quart saucepan over high heat. While the water heats, crack 4 of the eggs into separate cups or coffee mugs.

Reduce the heat to maintain a gentle simmer and then carefully slide eggs, 1 at a time, into the water. Poach the eggs until the whites are set and the yolks are still runny, about 2 minutes. Using a slotted spoon, transfer the eggs to a plate lined with paper towels, leaving space between them. Repeat with the remaining eggs. Don’t trim away any scraggly bits of egg white.

Toast the brioche until golden-brown and butter it.

Position a slice of toast in the center of each plate, top generously with mushrooms and put an egg on top of each slice. Sprinkle the eggs lightly with salt and pepper. Arrange the mushrooms on the plates and divide the Gruyere on top.

Garnish with sliced radishes.