In a small bowl, combine the warm water and instant dry yeast. Stir gently and let it sit for 5-10 minutes until foamy. This indicates the yeast is active.

In the bowl of a stand mixer fitted with the paddle attachment, whisk together the almond flour, vital wheat gluten, psyllium husk powder, erythritol, xanthan gum, and salt until well combined.

Add the foamy yeast mixture, three large eggs, melted butter, and 1/4 cup heavy cream to the dry ingredients. Mix on low speed until the ingredients are just combined. Increase speed to medium and mix for 5-7 minutes until a thick, cohesive dough forms. It will be much softer than traditional brioche dough.

Scrape down the sides of the bowl as needed. The dough should pull away from the sides slightly but will remain quite sticky.

Cover the bowl with plastic wrap or a damp kitchen towel and let the dough rise in a warm place for 60-90 minutes, or until it has noticeably increased in size (it may not double like traditional bread).

Lightly grease a 9x5 inch loaf pan and line it with parchment paper, leaving an overhang on the longer sides to easily lift the bread out later.

Gently punch down the dough to release air. Transfer the dough to a lightly floured (with almond flour) surface. Divide the dough into three equal portions.

Roll each portion into a log about the length of your loaf pan. Braid the three logs together and carefully place the braid into the prepared loaf pan.

Cover the loaf pan loosely with plastic wrap and let it rise in a warm place for another 30-45 minutes.

Preheat your oven to 350°F (175°C) during the last 15 minutes of the second rise.

In a small bowl, whisk together the egg yolk and 1 tablespoon heavy cream for the egg wash.

Brush the top of the risen brioche generously with the egg wash.

Bake for 35-40 minutes, or until the brioche is golden brown and sounds hollow when tapped. If the top browns too quickly, loosely tent it with aluminum foil.

Once baked, remove the loaf from the oven and let it cool in the pan for 10-15 minutes.

Using the parchment paper overhang, carefully lift the brioche out of the pan and transfer it to a wire rack to cool completely before slicing and serving. This is crucial for the texture to set.