Activate the yeast: In a small bowl, combine the warm milk and honey, then sprinkle the instant yeast over the mixture. Let it sit for 5-10 minutes until the yeast becomes frothy and activated.

Mix the dough: In a large bowl or stand mixer, whisk together 4 eggs, the frothy yeast mixture, 3 1/2 cups of flour, and kosher salt. Knead on medium speed until the dough comes together, about 5 minutes. Gradually add the softened butter in small chunks, kneading after each addition until fully incorporated.

Knead and add flour: Continue kneading, adding more flour as needed (up to 1/2 cup) until the dough is soft, smooth, and slightly sticky but not too wet. Knead for another 8-10 minutes.

First rise: Place the dough in a greased bowl, cover with a cloth or plastic wrap, and allow it to rise in a warm place for about 1-1.5 hours, or until doubled in size.

Incorporate the cold butter for flaky layers: On a floured surface, roll the dough into a large rectangle (about 10x14 inches). Arrange the cold butter slices evenly over one half of the dough, then fold the other half over to cover the butter. Pinch the edges to seal in the butter.

Roll and fold: Roll the dough out into another rectangle (similar in size to the first). Fold the dough into thirds like a letter (this is called laminating the dough, similar to making croissants). Cover with plastic wrap and refrigerate for 20-30 minutes to allow the butter to firm up.

Repeat rolling and folding: Repeat the rolling and folding process 2 more times, chilling the dough for 20 minutes between each fold.

Shape the loaf: After the final fold, roll the dough into a log and place it into a greased 9x5-inch loaf pan. Cover with a cloth and let it rise in a warm place for 45-60 minutes, or until it has doubled in size.

Preheat oven: Preheat the oven to 350°F (175°C).

Brush and bake: Brush the risen loaf with the beaten egg for a shiny, golden finish. Bake the brioche for 30-35 minutes, or until the top is golden brown and the internal temperature reaches 190°F (88°C).

Cool and enjoy: Allow the bread to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely. Slice and enjoy!