Preparation

• Position a rack in the center of the oven and heat the oven to 450°F.

  Heat 2 Tbs. of the oil in a 12-inch skillet over medium-high heat until shimmering hot. Add half of the mushrooms in a single layer and brown them on one side, 2 to 3 minutes. Flip the mushrooms and cook for 30 seconds more. Season them with salt and transfer to a plate. Repeat with 2 more Tbs. oil and the remaining mushrooms. Season them with salt and return the reserved mushrooms to the skillet. Add 2 Tbs. water, put the skillet in the oven, and roast until tender, about 5 minutes.

  While the mushrooms are cooking, bring 3 quarts of water, the vinegar, and 1/2 Tbs. 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 the eggs 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 each egg. Repeat with the remaining eggs. Trim away any scraggly bits of egg white.

  In a small skillet over medium-high heat, heat the remaining 1/2 cup oil and the garlic, stirring, until the garlic is light golden-brown, about 1-1/2 minutes. Carefully add the parsley (it will bubble) and immediately transfer the mixture to a small bowl.

  Toast the brioche until golden-brown and butter it.

  Divide the spinach among 8 large plates. Lightly season the spinach with salt and drizzle with some of the garlic oil. Position a slice of toast in the center of each plate, and put an egg on top of each slice. Sprinkle the eggs lightly with salt. Arrange the mushrooms on the plates and drizzle with the remaining garlic oil.

Make Ahead Tips

The mushrooms may be browned up to 3 hours ahead. Set aside in the skillet at room temperature. Add the water and roast shortly before serving.

The eggs may also be poached up to 3 hours ahead. Undercook them slightly (about 1-1/2 minutes) and then transfer to ice water to stop the cooking. When cool, arrange in a single layer on a tray lined with paper towels, cover with plastic wrap, and refrigerate. When ready to serve, reheat in gently simmering water, for about 1 minute.

The garlic oil may be made up to 2 hours ahead.