Bring water and 1 pinch salt in a saucepan to a boil; slowly stir in grits, stirring constantly. Reduce heat to low; simmer grits until tender and smooth, about 20 minutes, stirring often. Set aside and keep warm.

Heat olive oil in a large skillet over medium-high heat. Add ham; cook and stir until crisp. Stir in onion and bell pepper; cook until onion is translucent, about 4 minutes. Add shrimp; cook until just pink, 30 to 45 seconds. Transfer shrimp to a plate; set aside.

Pour wine into the skillet; stir, scraping the browned bits of food off the bottom of the skillet with a wooden spoon. Slowly add cream, reduce heat to low, and simmer until thickened, about 10 minutes. Season with salt and black pepper.

Divide grits between 2 serving plates; line edges of plates with 10 shrimp. Pour cream sauce over grits; sprinkle servings with green onions.