Preheat oven to 400 degrees F.
Heat the oil in a large skillet, over medium-high heat, until shimmering. Add the chorizo and cook, breaking it apart into smaller pieces with a wooden spoon, until browned, about 5-6 minutes. Remove with a slotted spoon and reserve.
Drain most of the chorizo fat from the skillet and return the skillet to the heat. Add the bacon and cook until golden brown, around 5 minutes. Remove with a slotted spoon and reserve with the chorizo.
Lower the heat to medium. Drain most of the fat again, leaving just a tablespoon or so in the skillet. Add the onion and garlic and sauté until softened and fragrant, 2-3 minutes. Add the sherry vinegar and paprika, stirring with a wooden spoon to deglaze the pan.
Add the bacon and chorizo back to the pan. Then, add the fire roasted tomatoes and mix to combine. Cook for a couple of minutes so all the liquid evaporates.
Remove the skillet from the heat and stir in the chopped parsley.
Add the softened cream cheese and stir until the cream cheese is melted and incorporated. Taste and season with salt and pepper.
Combine both cheeses in a bowl. Add 2/3 to the skillet, mixing to combine.
Transfer the dip to an oven safe dish and place on a baking sheet. Top with the remaining cheese and bake for 30 minutes or until the dip is heated through and the cheese has melted.
Garnish with chopped chives and serve immediately!