These over-the-top eggs are ready for the weekend.
Using a serrated knife, slice the crust off the brioche and cut into 1-inch-thick strips. Crack the eggs into a medium bowl, season with salt, and whisk until homogenous and no streaks of white remain. Warm two serving bowls in a low oven.
In a 10-inch skillet over medium heat, melt 1 tablespoon butter until foaming. Add the brioche strips and fry until golden-brown, 1 minute. Flip bread, add another tablespoon of butter, and fry the other side, 1 minute. Remove skillet from heat, lightly season with salt, and set aside . In a 2-quart saucier over medium-high heat, melt 1 tablespoon of butter until foamy. Add the eggs, and reduce heat to medium-low. Cook, whisking constantly, until the eggs begin to look thickened with lots of small curds running throughout, about 1 to 2 minutes. Add the remaining 1 tablespoon of butter and whisk until melted. Remove from heat, whisk in the crème fraîche, and divide between warmed bowls.
Drizzle the eggs with maple syrup, sprinkle with black pepper, and dollop with trout roe. Serve immediately with brioche soldiers alongside.