Put oil and onion in a large pot over medium-high heat. Cook until fragrant, about 1 minute. Add favas, salt, sugar, and 1/4 cup water. Bring to a simmer. Cover and cook, stirring occasionally, 20 minutes.
Add 1/4 cup dill, cover, and cook until fava pods are tender and starting to fall apart, about 10 minutes. Sprinkle with 1 tbsp. dill and serve warm or at room temperature, with yogurt on the side.
Note: Nutritional analysis is per serving, without yogurt.