In a large saucepan over medium, heat oil. Add onion, bell pepper, garlic, cumin, salt, and black pepper. Cook, stirring occasionally until onion has softened about 5 to 7 minutes. Slowly whisk in the milk, tomato paste, and vinegar, until well combined; allow to steep for 20 minutes.
In a large heatproof bowl, combine grated cheeses, tomatillo salsa, lime juice and oregano. Place a fine mesh strainer over the bowl containing the cheese. Strain milk mixture into the bowl. Discard solids from strainer.
Using a wooden spoon stir cheese mixture until smooth and saucy. If cheese doesn’t melt completely, set bowl over a pot of simmering water and stir until cheese melts and mixture comes together. Transfer to a bowl and serve immediately.