Preheat an oven to 450 degrees F (230 degrees C). Prick sweet potatoes several times with a fork and place onto a baking sheet.
Bake in the preheated oven until potatoes are easily pierced with a fork, 50 minutes to 1 hour.
At the same time, bring water and brown rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 45 to 50 minutes.
Remove sweet potatoes from the oven and remove skin when cool enough to handle.
Place sweet potato flesh and cooked rice in a food processor. Add soy milk, maple syrup, cinnamon, nutmeg, and vanilla; process until smooth. Serve hot, warm, or chilled.