In mini food processor, spice blender or mortar with pestle, mash garlic, lemongrass, ginger and chile paste until paste forms (or finely mince with knife).
In large saucepan, heat sesame oil over medium heat. Add onion and cook until golden, stirring occasionally, about 7 minutes. Add paste mixture (or minced ingredients) and stir until fragrant, about 30 seconds. Add sweet potatoes, broth and coconut milk and bring to a boil. Reduce heat to low and simmer until potatoes are very tender, about 20 minutes. Stir in salt and garnish with peanuts.