- In a food processor, process the chopped walnuts, stopping to scrape down the sides of the bowl two or three times, until they become a smooth, thick paste. Set aside.
- Heat the olive oil in a large saucepan over medium-high heat. Add the onion and cook, stirring occasionally, until translucent, about 3 minutes. Sprinkle the flour over the onions and cook, stirring occasionally, until golden brown, about 4 minutes. Add the walnut butter and vinegar; whisk until smooth.
- Slowly whisk in the vegetable stock and continue whisking until no lumps remain. Stir in the cinnamon, cloves, sugar, milk, salt, and pepper; bring to a boil.
- Reduce the heat to a simmer and cook, stirring occasionally, until the flavors have melded, 15 minutes.
- Stir in the cotija cheese and continue simmering, stirring occasionally, 15 minutes more.
- Remove from the heat and stir in the cilantro.
*NOTE: The sauce may be prepared ahead of time and gently reheated.