Preheat the oven to 350° In a large saucepan, cover the eggs with water and bring to a simmer. Cook over moderate heat for 8 minutes. Drain the eggs, return them to the pan and shake the pan to crack the shells all over. Fill the pan with cold water and let the eggs cool for 3 minutes. Drain and peel the eggs; pat dry.
Meanwhile, in a small bowl, blend together the mayonnaise, garlic and one-third of the minced anchovies.
In a small skillet, melt the butter over moderate heat. Add the remaining minced anchovies and cook, stirring, until they break down, about 1 minute. Stir in lemon zest and brioche crumbs and transfer to a rimmed baking sheet. Bake the crumbs until golden brown and crisp, about 2 minutes.
Halve the eggs and arrange on a platter. Dollop 1/4 teaspoon of the mayonnaise on each egg yolk. Top each with the anchovy crumbs and parsley and serve.
The hard-cooked eggs and anchovy mayonnaise can be refrigerated separately overnight.