Combine the flour, eggs, salt, granulated sugar, yeast, and milk and mix on low speed with a dough hook attachment for 4 minutes with 62g / 2.19oz of the butter. Mix on high speed for 4 minutes. Start adding the rest of the butter in 4 stages while the mixer is on, scraping down the sides of the bowl between each addition to the dough should achieve full gluten development, 30 to 45 minutes. Cover and place in the refrigerator overnight.
Prepare a 38-cm / 15-in Pullman loaf pan by spraying it with nonstick cooking spray.
Shape the dough into a bâtard loaf and place inside of the prepared mold. Place the lid over the mold and proof at room temperature for about 2 hours, or until doubled in size.
Meanwhile, preheat a convection oven to 190°C / 375°F.
Bake until the internal temperature of the loaf is 95°C / 200°F (use a probe thermometer to check the temperature, sliding the lid off the loaf pan just enough to fit the probe).
Once it is baked, remove the lid from the pan and unmold the baked loaf onto a cooling rack (do not let the brioche cool off in the pan, or it will shrink).
When the loaf has cooled, freeze it for 2 hours so that it will be easier to cut.
Trim the crust off the loaf and cut into a small dice. Place diced brioche in a bowl and toss with 200g / 7.05oz confectioners’ sugar until it has coated the brioche evenly.
Spread the diced brioche onto a parchment paper–lined sheet pan in an even layer.
Toast in a 300°F / 148°C convection oven at until golden brown and crisp. Cool on the sheet pan.
Reserve at room temperature in an airtight container. Discard after 4 days.