To the bowl of a stand mixer, add your gluten-free flour, sugar, salt, psyllium husk, and instant yeast. Whisk by hand until everything is mixed together.
Fit your bowl onto the stand mixer with the paddle attachment and turn on low speed. Add in your softened unsalted butter cut into pads one at a time, then add 3 eggs and the extra egg yolk, also one at a time.
Once mixed, slowly pour in your warm milk and allow the mixer to continue to stir gently until everything is incorporated.
Mix on medium speed until your dough, which will resemble cake batter, looks smooth.
Butter an 8 ½ x 4 ½ loaf pan. Use a large cookie scoop or spoon to scoop the batter into the loaf pan, creating lumps and valleys, which create that signature look on the top of brioche bread.
Cover with plastic wrap and allow the bread to rise on the counter until it almost reaches the top of the loaf pan. The time will depend on many factors, such as temperature and humidity, but try 45 minutes to an hour first and then check on it in 10-minute intervals until it reaches the correct height. Mine took about an hour to rise.
Preheat the oven to 350°F, and while it’s preheating, gently brush the top of your loaf with an egg wash made from the remaining egg.
Bake your bread for 30 minutes, until a cake tester comes out clean, and allow it to rest and cool in the loaf pan for about 30 minutes before removing it.
Allow the loaf to rest until cool, then cut and enjoy with butter, jam, honey, or all of the above!
Notes
Make an egg wash by beating one egg and brushing it over the top of the loaf before baking.
To Store: Store at room temperature for up to 5 days in an airtight container. It'll stay fresher in the refrigerator for longer, up to 7 days.
To Freeze: Wrap slices in plastic wrap and store in the freezer for up to 3 months. Defrost at room temperature.