Combine warm water, active dry yeast, and inulin in a small vessel; whisk gently and allow to sit for 10 minutes until a thick foam forms.

In a large bowl, sift and whisk together the vital wheat gluten, lupin flour, oat fiber, coconut flour, allulose, baking powder, xanthan gum, and salt.

Incorporate the cold, cubed butter into the dry mixture using a pastry cutter or fork until butter pieces are roughly the size of peas.

Add the bloomed yeast mixture, cold water, and heavy cream to the flour-butter mixture; stir with a spatula until a shaggy dough forms, ensuring butter chunks remain intact.

Wrap the dough tightly in plastic film and refrigerate for 30 minutes to chill the fats and hydrate the fibers.

On a surface lightly dusted with vital wheat gluten, roll the chilled dough into a 12x6 inch rectangle. Perform a letter fold by folding the top third down and the bottom third up.

Rotate the dough 90 degrees and repeat the rolling and folding process twice more to create internal lamination layers, then refrigerate for 30 minutes.

Preheat the oven to 375°F (190°C) and line a baking sheet with parchment paper.

Roll the chilled dough to 1/4 inch thickness and use a pizza cutter to slice the dough into 8 elongated triangles.

Roll each triangle tightly from the base to the tip and curve the ends slightly to form a crescent shape; place on the prepared baking sheet.

Whisk the egg with 1 tsp of water and brush the tops of the croissants thoroughly.

Bake for 22 to 25 minutes until the pastry is deep golden brown and firm to the touch.

Transfer to a wire rack and allow to cool for at least 20 minutes to set the internal structure before serving.