Add the milk, water, salt, and pepper to a sauce pot and bring to a simmer. Whisk in the grits and turn heat to low. Simmer on low, stirring occasionally, for about 25 minutes.
Remove from heat and allow to cool a few minutes. Stir in half of the butter and all the cream cheese.
Pour into a bowl and stir in the chorizo, pico, and cheese. Make sure it is fully cooled, then you can crack in the eggs. Add a small pinch of salt with the eggs, but between the salt in the grits and the salty chorizo and cheese you should be at a good place with the seasoning.
Preheat the oven to 400.
Put a small oven safe pan over high heat and add in the other half of the butter to melt. When the butter is starting to darken, add in the grits mixture. Get the pan into the oven and bake for about 35 minutes until full set.
Serve with the garnishes, and any other garnishes you might like. More pico would work, or some cilantro.