Heat oil in a large frying pan over high heat. Add shallots, onions, and garlic and cook, stirring often, until fragrant, about 1 minute. Add spinach and cook, stirring often, until wilted, about 2 minutes.
Using a slotted spoon, scoop spinach into a food processor; pulse until roughly puréed, about 5 pulses. Add remaining ingredients except pepper, pulse once just to combine, then season to taste with pepper.
Note: Nutritional analysis is per serving.