Remove the yam skin, slice the yam width-wise into ½ inch thick pieces and wash them under running water.
Place the yams in a bowl, add warm water to cover the yams and let it rest for 30 minutes to reduce some of the starchiness.
Place the butter in a frying pan, add the minced garlic, black pepper, and fresh thyme to the butter and cook on low-medium heat until the butter is browned, about 3 minutes.
Remove the frying pan from the heat and pour the butter mixture into a small bowl.
Place the onion slices in the frying pan, leaving the butter residue in the pan. Add salt to taste and caramelize the onions on low-medium heat for 10 minutes.
Drain the water from the yams, add salt and 1 tablespoon of the brown butter to the yams and mix everything together.
Oil a baking pan, place the yams on the pan and bake on each side for 15 minutes at 350°F (175°C) or until the yams are golden brown on each side.
Scoop the baked yams onto the frying pan with the caramelized onions. Pour the rest of the brown butter onto the yams and combine everything together. Place the frying pan in the oven for 5 minutes or until everything is heated to your liking.