Preheat oven to 350˚F (180˚C).
In a medium bowl, fold together the cream cheese, shredded Monterey Jack cheese, and sour cream. Set aside.
In a large skillet, drizzle olive oil over medium heat.
Add the onions and cook, stirring occasionally, until softened.
Add the garlic and cook just until fragrant, 30 seconds to 1 minute.
Crumble in the fresh chorizo and cook, stirring often and breaking up with a spoon into small pieces, until browned, about 5 minutes.
Stir in the paprika, oregano, salt, and pepper, followed by the diced tomatoes and spinach.
Reduce heat to medium low and cook, stirring occasionally, until most of the liquid has evaporated.
Remove from heat and allow to cool briefly, until no longer bubbling.
Add 3/4 of the cheese mixture to the chorizo, stirring until melted and evenly blended. Adjust seasonings to taste, adding more salt and pepper if needed.
Transfer the chorizo mixture to one larger or multiple individual oven-safe baking dishes. Top evenly with dollops of the remaining 1/4 cheese.
Place the baking dishes on a rimmed baking sheet (just in case any cheese bubbles over) and transfer to the preheated oven.
Bake until the cheese is bubbly and golden, 25-30 minutes.
Serve the dip warm with toasted bread, crackers, or tortilla chips.