Bring water and milk to a boil.

Add salt and turn off heat.

Sift polenta into the hot liquid while whisking.

Turn heat to low and cook, whisking occasionally, for 30 minutes, until polenta thickens.

Dice chorizo and add to a medium skillet with olive oil.

Slowly bring the heat to low and render the fat without crisping the chorizo.

Push chorizo to the side, turn heat to medium-high, and add shrimp.

Sauté shrimp until they get some color.

Add white wine to deglaze the pan, scraping up brown bits.

Add tomatoes and red peppers, and turn up the heat to reduce the sauce.

Cook until shrimp are firm and opaque.

Add parsley and arugula and taste for seasoning.

Stir butter and Parmesan into the polenta.

Spoon polenta onto serving dishes.

Top with shrimp and chorizo mixture and serve immediately.