Place sweet potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until fork-tender, about 10 minutes. Drain.

Combine olive oil and flour in a heavy pot over medium-low heat; cook, stirring constantly, until a smooth paste forms and turns a light caramel color. Add broth and brown sugar. Bring to a boil, then reduce heat to a simmer. Stir in sweet potatoes, onion, turmeric, cinnamon, cloves, and red pepper flakes. Bring back to a simmer and cook for 5 minutes more.

Remove soup from heat and allow to cool slightly. Fill a blender halfway with soup. Cover and hold lid down with a potholder; pulse a few times before leaving on to blend. Pour into another pot. Repeat with remaining soup.

Mix soy milk into the pureed soup and heat until warmed through, 5 to 10 minutes. Season with salt. Add chicken and carrots for more texture.