Fresh ginger is very easy to grate with a small side of a grater or a microplane when it's frozen. Peel it first by scraping the skin away with the edge of a spoon. I always keep a nub of ginger in the freezer sealed in a small ziplock bag.
Chop sweet potatoes into roughly 1.5" pieces and transfer to a medium saucepan along with chopped garlic. Add enough water to cover the sweet potatoes about half way.
Bring to a boil over heat high, reduce heat to medium low, cover and simmer for about 12-15 minutes until potatoes are easily pierced through with a sharp knife. Strain potatoes and garlic.
Add ginger, sesame oil and stock or water and use an immersion blender to 'mash' the sweet potatoes until smooth. If you prefer it a little chunky that's okay too of course. You may need a little more stock/water if you're looking for an extra smooth 'mash'.
Season to taste with salt and pepper (you will need less if using stock) and serve.