Peel and thinly slice the yams.
In a medium bowl, mix the sugars, spices, and salt. Rub butter on the inside of a deep baking dish. Place a piece of parchment paper at the bottom and layer yams in an overlapping pattern. Sprinkle some sugar and spice mixture evenly on top of the yams. Add another layer of yams and sugar and spice mixture.
In a medium pan over medium heat, heat the almond milk and brown butter until hot, about 3 minutes. Pour this mixture over the yams.
Preheat oven to 350°F. Put a piece of parchment on top of the baking pan and put another baking dish the same size on top. Put a weight inside the top baking dish, such as a brick or a small cast-iron pan. Place baking pan on a larger, deep-sided tray filled halfway with water and bake for 1 1⁄2 hours, or until yams are tender.
Transfer yams to a refrigerator and cool overnight. Remove from the pan and cut into 3-by-1 1⁄2-inch slices.
Make the candied pecans: Reduce oven heat to 325°F. Whisk the egg white in a large bowl until frothy, then add the pecans and mix. Add the sugar, cinnamon, and salt, and stir to combine. Spread pecan mixture on a baking pan lined with a nonstick silicone baking mat and cook at 325°F, stirring every 10 minutes, until it is browned and crisp but not burnt, about 30 minutes.
Make the brown-butter almond milk: Combine brown butter, milk, and salt in a saucepan over medium heat and cook until hot, about 3 minutes.
Remove gratin from the refrigerator. Oil a griddle and sear gratin slices in batches over high heat until browned, about 2 minutes a side. Place two pieces in a bowl, add brown butter-almond milk, garnish with pecans and Maldon salt.