Combine all dry ingredients in a mixing bowl of a stand mixer fitted with a dough hook.

On medium-low speed, add egg, then gradually add milk to incorporate with the mixture.

Continue on that speed, slowly add melted butter to the flour mixture and mix until cohesive dough starts to form. About 2 minutes.

Make sure there is no dry flour that remains. Scrape down the sides of the bowl with a spatula if needed.

Increase the speed to medium and continue kneading the dough until smooth and elastic and pull away from the sides of the bowl completely. Approximately 4 to 5 minutes.

The dough is supposed to be a little bit wet due to the generous amount of butter and milk called for.

Transfer the dough to a lightly floured surface. Start kneading with your hands.

If the dough is too sticky to handle, add more flour to your hands before kneading.

Use your hands and gently lift and fold the edge of the dough that's farthest away from you toward the middle.

Turn the dough 90 degrees and fold the other edge toward the middle again.

Repeat the process of turning and folding the dough.

Continue to knead until the dough forms a smooth, round ball, about 1 to 2 minutes.

Turn the dough seam side down in a lightly greased or lined with plastic wrap large mixing bowl.

Cover tightly and let it proof until the dough is double in size, approximately 1.5 to 2 hours.

Press down the dough and deflate. Transfer the dough to a lightly floured surface.

Divide the dough into 2 equal pieces.

Work with 1 dough at a time. Make sure to cover the other dough with plastic wrap to prevent it from drying out.

Grease your baking pan.

Press and stretch the dough into a rectangle. Try to use your hands instead of a rolling pin to avoid overworking your dough.

Roll the dough away from you into a loose cylinder, tuck the sides of the dough as you go.

Pinch the seam with your fingers to secure the dough.

Place the dough seam side down. Then carefully transfer it to your baking pan.

Repeat the process with the remaining piece.

Cover the pan tightly with plastic wrap and let the shaped dough proof a second time until it's double in size, approximately 1.5 to 2 hours.

Preheat oven to 350F.

Gently brush the top of the unbaked brioche with egg wash mixture.

Bake until the loaf turns deep golden brown color, approximately 40-55 minutes; remember to rotate the baking pan halfway through the process.

Let the loaf cool in the pan for 15 minutes before unmolding it. 

Brush the top and the side of the brioche loaf with extra melted butter (if desired).

Let the loaf cool down completely before serving.