Cut the chorizo into quarter-inch pieces.
Heat the water in a big pot until it boils. When the water comes back to a boil, add the salt and steel-cut oats and stir continuously.
Once the oats are soft, reduce heat and simmer, covered, for 25 minutes, stirring now and again.
Add chicken broth, cover, and boil until mixture is creamy, about 5 minutes. Avoid overcooking.
When the cheese is melted, add 6 tablespoons of parmesan cheese and mix.
In the meantime, cook the chorizo and broccoli in olive oil in a big, nonstick skillet until the chorizo is browned. Add the tomatoes, pepper, and the last 1/8 teaspoon of salt and stir.
Spoon risotto onto four plates; garnish with broccoli and chorizo.
Add the reserved cheese and fresh parsley on top.