Step 1Melt the butter in a large saute pan over medium-high heat. Add the ham and cook until browned, about 5 minutes. Add the onion, green pepper, mushrooms and thyme, and cook until the onion is translucent, about 5 minutes.
Step 2Add the Madeira, coffee, chicken broth and tomato and bring to a light boil. Stir in the cornstarch mixture. Reduce the heat and simmer the sauce until it reduces by one-third, about 10 minutes.
Step 1In a saucepan, combine the milk, cream and butter. Bring to a light simmer. Slowly stir in the grits, reduce the heat to low and stir frequently until the grits are thick and creamy, about 10 minutes.
Step 2Stir in the cheese and the salt and pepper to taste. Keep warm.
Step 1Heat 1 tablespoon butter in another large saute pan. Add the shrimp and cook until pink, about 3 minutes.
Step 2Add the red-eye gravy. Add the remaining butter and stir to incorporate.
Step 3To serve, divide the warm grits among 6 plates and top with the shrimp and gravy. Garnish with the cheese and chives.