Preheat oven to 425 degrees F.
Butter a nonstick regular size muffin tin with 12 muffin cups or 2 (6-muffin) cups.
For the polenta:
In a medium-sized stock pot over medium heat, bring the milk and stock to a bubble.
While the liquids are heating up place a small skillet over medium-high heat with 1 turn of the pan of olive oil, about 1 tablespoon. Add the chorizo and cook until crispy 2 to 3 minutes.
Once the liquids come up to a bubble slowly whisk in the polenta and continue whisking until it begins to thicken and resemble hot oatmeal about 3 to 4 minutes. Turn off the heat and add in the cheese, chopped parsley, 2 tablespoons butter and crispy chorizo. Pour the polenta into the muffin tins, 1/2 of the way up the muffin cup.
Once all the cups are filled, form a well with the back of a spoon by pushing the polenta up the side until it reaches the top rim of the muffin tin. The well will be relatively large but that's ok, you want the egg to have a little nesting place so it won't overflow out of the tin. Once you have made all the wells, crack an egg into each of the polenta filled cups. Season the tops of the eggs with some salt and pepper. Transfer to the oven and bake for 20 minutes; yolk will still be a little runny. Once done, remove from the oven and let sit. Run a small butter knife around the edges of the polenta to loosen from the sides of the muffin tin. Gently help them out of the muffin tins with a fork or a knife and serve plated or on a platter.