Pour 2 cups of the chicken broth, the whole milk, 3 tablespoons of the butter, and a pinch of salt into a medium pot and bring the mixture to a gentle boil. When small bubbles cover the surface, slowly whisk in the stone-ground grits until no dry pockets remain.
Lower the heat and cook the grits for 10-15 minutes, whisking every few minutes. They are ready when the grains are tender and the mixture looks creamy rather than stiff; cover and remove from the heat.
Cook the bacon in a nonstick or cast iron skillet until crisp, then transfer it to a paper towel lined plate and chop it once cool. The skillet should smell smoky and show browned bits where the bacon rendered.
Pour off the bacon fat, leaving 2 tablespoons in the skillet. A thin layer of drippings should coat the pan without pooling heavily around the edges.
Rinse the shrimp with cold water, dry them well, and season with kosher salt and black pepper, using little or no added salt if they were treated with sodium. Sear the shrimp in the bacon drippings for about 2 minutes per side, until pink, opaque, and curled into a loose C-shape.
Add the remaining tablespoon of butter and 1/2 cup chicken broth to the skillet, then stir around the shrimp until the butter melts and the broth heats through. The browned bits should loosen from the pan and the sauce should develop a light glossy sheen.
Stir the sharp cheddar cheese into the resting grits and taste for salt. The cheese should disappear into the grits, leaving a smooth, creamy surface without oily puddles.
Spoon the shrimp and skillet liquid over the grits, then finish with chopped bacon and thinly sliced green onions, if using. Serve while the grits are loose and the bacon still has crunch.