In a large skillet, heat the bacon grease over moderate heat, add the onion, bell pepper, and garlic, and stir till softened, about 8 minutes.
Add the chicken or turkey and potatoes and stir for 5 minutes longer. Add the cheese, parsley, tarragon, salt and pepper, and stir untill well blended.
Using a heavy spatula, press the mixture down and let it cook till a brown crust forms on the bottom, about 10 minutes.
Using two heavy spatulas, carefully flip the hash over in the skillet and cook till the other side is nicely crusted, 8 to 10 minutes.
Slide the hash onto a plate, cut into 4 portions, and serve immediately.