In a medium saucepan, bring the chicken broth and milk to a gentle boil over medium-high heat. Slowly whisk in the grits and a pinch of salt. Reduce the heat to low, cover the pot, and simmer for 20 to 25 minutes. Stir occasionally to prevent sticking. Once the grits are creamy and tender, stir in 2 tablespoons of butter and the shredded cheddar cheese until melted and smooth.
While the grits are simmering, place the cleaned shrimp in a medium bowl. Sprinkle the Cajun seasoning over the shrimp and toss them thoroughly to ensure every piece is well-coated. Let the shrimp sit for about 5 minutes to allow the spices to penetrate the meat.
Heat the olive oil and 1 tablespoon of butter in a large skillet over medium heat. Add the diced onion and green bell pepper. Sauté for about 5 minutes or until the vegetables have softened. Add the minced garlic and cook for an additional 1 minute until fragrant, being careful not to burn the garlic.
Turn the heat up to medium-high and add the seasoned shrimp to the skillet with the vegetables. Cook the shrimp for 2 to 3 minutes per side, just until they turn pink and opaque. Do not overcook them, as they can become rubbery very quickly.
Lower the heat and add the remaining tablespoon of butter and the lemon juice to the skillet. Stir gently to deglaze the pan, scraping up any flavorful browned bits from the bottom. This creates a light, spicy sauce that coats the shrimp and vegetables beautifully.
Taste the shrimp and grits separately, adding salt or pepper if needed. Spoon a generous portion of the creamy grits into shallow bowls. Top with the Cajun shrimp mixture and a drizzle of the pan sauce. Garnish with fresh green onions and serve immediately.