Prepare the yams: Scrub, peel, and slice the sweet potatoes into 1/2-inch thick rounds. Set them aside.
Combine ingredients: Place the sliced yams into a medium pot over medium-high heat. Add brown sugar, white sugar, cinnamon, nutmeg, ginger, salt, vanilla extract, butter, and orange juice concentrate. Stir to coat the yams evenly with the sugar and butter mixture.
Cook the yams: Let the mixture come to a gentle boil. Cover the pot and reduce the heat to low. Simmer for about 50 minutes, stirring occasionally, until the yams are fork-tender.
Create the syrup: Remove the lid, increase the heat to medium, and let the cooking liquid boil uncovered for about 10 minutes, stirring occasionally. The liquid will reduce into a thick, caramel-like syrup that coats the yams beautifully.
Serve warm: Remove the pot from heat. Transfer the candied yams to a serving dish or keep them warm in the oven until ready to serve. These taste best when served warm.