In a large bowl cream the coconut oil and sweetener together until very smooth. Sift the baking soda, spices, salt, and egg white protein into the almond and coconut flour, then slowly add the almond flour mixture into the coconut oil mixture. Mix until well combined, then slowly add water just until the dough is soft, yet able to roll out. Form into a tight ball and cool in the fridge to chill.
Preheat oven to 325 degrees F. Place the dough onto a non-stick surface (I used parchment paper), then top it with another piece of non-stick surface (again, I used parchment paper) roll the dough out into about 1/4 inch high. Cut the dough with cookie cutters, and place onto a baking sheet. Bake for 20-30 minutes (depending on the size of the shape) or until golden brown.
To make the icing, combine all ingredients in a bowl and mix with a hand mixer until well incorporated. Add food dye as desired. Set aside.
To assemble: Decide how you want your house to be positioned on the base. Make sure the base is big enough so you will have plenty of space for a front walkway, bushes along the side of the house, a backyard, etc. Lay your walls down on the base where they will go. Pipe a line of icing in an L shape for two adjoining walls, as well as a strip of icing along the inside edge of one wall. Carefully stand the walls up and hold in place a few minutes until stable. Repeat steps 4-5 for the other sides of the house. Let the icing dry and harden before attaching the roof. Pipe a line of icing all along the top edge of the walls. Gently place the two roof pieces on the house simultaneously. Hold the roof in place for a few minutes until the roof is stable. Then pipe a strip of icing along the ridgeline. Wait for the icing to dry and harden completely before decorating the house.