In a medium saucepan, melt butter over medium heat. In a small bowl or a cup, whisk the arrowroot powder with 2 tablespoons of the half and half until arrowroot is dissolved and there are no visible lumps. Add the arrowroot mixture to the melted butter over medium heat and whisk together. Slowly add the remaining half and half stirring constantly. Continue to stir and heat until the mixture thickens (this can take a while, but keep stirring to keep the arrowroot from sticking to the bottom and burning). Add the grated cheeses and stir to melt and combine. Add sea salt and pepper to taste. Remove from heat and serve with gluten free noodles, or on cooked veggies immediately. NOTE: For best results, do not reheat or reuse.  Reheated sauce will be too runny.