Heat oil in a large pot over medium-high heat. Add sweet potatoes and cook, stirring occasionally, until slightly softened and lightly charred, 6 to 7 minutes. Add onion and poblanos; cook, stirring occasionally, until slightly softened, about 3 minutes. Add garlic, chili powder and cumin; cook, stirring constantly, until fragrant, about 30 seconds. Add broth, tomatoes, green chiles and 1 cup water. Cover, increase heat to high and bring to a boil.