Place the shredded mozzarella and cream cheese in a medium microwave-safe bowl, then heat until fully melted and stir until smooth. The cheeses should form one glossy mixture with no separate firm pieces remaining.

Move the warm cheese mixture to a food processor and add the large egg, almond flour, baking powder, xanthan gum, and salt. Process promptly so the cheese stays warm and blends evenly with the dry ingredients.

Process until the dough comes together, stopping to scrape down the bowl with a rubber spatula if needed. The finished dough should feel slightly sticky but smooth, with no dry flour pockets.

Lightly oil your hands, place the dough on parchment paper, and knead it into a round ball. Stop when the surface looks smooth and the dough no longer clings heavily to your hands.

Divide the dough into four equal pieces and gently knead each piece into a compact portion. The pieces should feel firmer as they cool slightly, which makes them easier to roll.

Roll each portion into an approximately 20-inch strand on parchment, dusting lightly with almond flour only if needed, then pinch the four strands together at one end. Aim for even thickness from end to end so the braid bakes uniformly.

Starting near the sealed end, cross the left pair over the right pair, then bring the right pair over the left pair and continue alternating until braided; pinch the far end closed. Keep the strands close together and tuck any small cracks underneath as you work.

Brush the braid with egg yolk, scatter sesame seeds over the top, and bake at 350°F/175°C for 20 minutes. The loaf is ready when it is deeply golden and the braid feels set rather than soft in the center.

Transfer the baked challah to parchment paper and let it cool completely before slicing. Cooling lets the interior firm up, preventing a dense or gummy cut surface.