Peel the sweet potatoes and cut them into 1.5-inch cubes.
Place them in a pot, cover with water, and bring to a boil. Cook for 25 minutes, or until they're very soft.
Drain the sweet potatoes well and place them in a large mixing bowl. Add butter, brown sugar, and mash (using a regular potato masher) until the butter has melted into the potatoes.
Slowly add coconut milk and whip until smooth and creamy, using a whisk or spatula. Then add ginger, nutmeg, allspice, and vanilla. Continue whipping until fully combined. Add a few pinches of black pepper and touch of salt if needed.
Transfer the sweet potatoes to a serving dish and top with fresh thyme and a slice of room temperature butter (optional).