In a large pot, heat oil over medium-high heat. Add chorizo and cook, stirring, for 3 to 4 minutes or until browned. Using a slotted spoon, transfer chorizo to a plate lined with paper towels.
Add onions to the pot and cook, stirring, for 6 to 8 minutes or until softened. Add garlic and kale; cook, stirring, for 1 minute.
Stir in potatoes, teff and broth; bring to a boil. Reduce heat to medium-low, cover, leaving lid ajar, and simmer, stirring occasionally, for 15 to 20 minutes or until potatoes and teff are very tender. Use a wooden spoon to coarsely break up about half of the potatoes.
Return chorizo to the pot and stir in tomatoes; simmer, uncovered, stirring occasionally, for 5 to 10 minutes or until soup is slightly thickened. Season to taste with salt and pepper.