For the grits, bring the chicken broth and pepper to a boil.
Add the grits to the broth and cook covered over low-medium heat for 1 hour, stirring frequently. Add water ¼ cup at a time as needed during the cooking to keep the grits from sticking.
During the last 15 minutes of cooking, add the Parmesan cheese and stir to allow it to dissolve into the grits.
For the onions, pour the olive oil in a skillet over low-medium heat and add the onion and salt. Cook for 15 minutes until caramelized.
Preheat the oven to 400 degrees. Spread the shrimp on a greased baking sheet.
Mix the olive oil, garlic, and rosemary and pour over the shrimp. Roast the shrimp for 8 to 10 minutes.
Ladle the grits into large bowls and divide the onions and shrimp evenly among the grits.