Preheat grill to medium-high. Bring milk and 4 cups water to a boil in a medium saucepan over medium-high heat. Stir in 2 1/2 teaspoons salt. Slowly add grits, whisking constantly. Reduce heat, cover, and simmer, stirring occasionally, until thick and creamy, about 15 minutes. Stir in cheese. Remove from heat; cover to keep warm.

Meanwhile, cook chorizo in a medium skillet over medium-high heat, stirring and breaking into small pieces, until browned and crisp in spots, about 5 minutes. Transfer chorizo and rendered oil to a bowl; cover to keep warm.

Toss shrimp with olive oil and season generously with salt. Grill, flipping once, until lightly charred in spots and opaque, 4 to 5 minutes.

Stir grits, adding hot water a few tablespoons at a time if needed to make smooth again. Divide grits, chorizo (use a slotted spoon), and shrimp among bowls; drizzle with chorizo oil, top with cilantro, and serve with salsa.