I have a lot of sassafras growing, and they drop a lot of branches. I have been piling them up and burning them, and using the ashes in the garden. Is there a way to use the branches like propagation or flavoring with them instead of burning them?
Hugelkultur is a sort of slow composting process that uses woody material as the bottom layer of a sheet compost.
In a nutshell: pile up the branches (don't shred or chip them), pack down the pile a bit, cover the pile with compost and/or soil, add a layer of mulch on top. Let it rest for a couple of months, and then plant into it.
Decaying wood acts like a sponge, so the pile should retain moisture so that the plants you are growing in the pile don't need (as much) watering. As the wood decomposes it will heat up, so your plants may gain some benefit in the shoulder months from slight bottom heat.
Wikipedia covers the culinary uses of the Sassafras plant:
Roots (Pathogenic and carcinogenic)
As for the cooking aspect of sassafras, 'When ground, they smell somewhat like eucalyptus or juicy fruit gum'. The powder is used to flavour soups and stews and acts as a thickener when combined with liquid.
Source: The Spice House