Prepare the grits by bringing milk, butter, and salt to a boil in a saucepan.

Add stone-milled grits to the boiling mixture.

Reduce heat to low and cook for 25 minutes, stirring constantly to prevent sticking.

Remove from heat and keep warm.

In a separate large skillet, saute the shrimp in olive oil until they start to turn pink and opaque.

Add the andouille sausage and tasso ham to the skillet with the shrimp.

Deglaze the pan with white wine, scraping up any browned bits from the bottom.

Let the wine reduce until almost completely evaporated.

Reduce the heat to low and slowly whisk in the diced butter, one piece at a time, until fully incorporated and the sauce is emulsified.

Ensure the sauce does not boil, as this will cause the butter to separate.

Stir in the fresh chives.

Divide the warm grits evenly between two warm plates.

Arrange the sauteed shrimp, andouille sausage, and tasso ham evenly over the grits on each plate.

Spoon the sauce over the shrimp and grits, ensuring each plate receives a generous portion of sausage and ham.

Serve immediately.