Heat a cast iron skillet or griddle over medium-high heat.
Grind the chorizo in a food processor into very small crumbles. Place the ground chorizo and ground pork in a bowl and season with Worcestershire, smoked paprika, salt and pepper. Add a drizzle of extra-virgin olive oil to the meat mixture and combine. Form 12 patties that are thinner at the center than the edges. Cook the sliders 3 minutes per side. Pile shredded cheese onto the burgers for the last minute of cook time to melt.
Meanwhile, place the avocados in a food processor. Add the lemon juice, garlic, cilantro, if desired, and cream, and process until very smooth and mayo-like in consistency.
Serve the sliders on rolls topped with lettuce, tomato, onion, and avocado cream sauce.