As I mentioned above, any sort of livers and naughty bits will work here. I normally use duck or goose giblets, but upland game bird giblets are excellent, as would ground deer liver and heart. The trick to good dirty rice, at least to me, is to get a succession of crusts on the bottom of the frying pan that you scrape away with a wooden spoon. Each crust adds a little more flavor; it's a technique you see a lot in Italian sugos, which are long-cooked pasta sauces.
1/2to 1 cup livers from birds,or about 3 ounces deer liver
1/2to 1 pound of ground meatfrom gizzards and hearts or any other ground meat
1 1/2cupsmeat broth
1/2cupfinely chopped onion
2celery stalks,finely chopped
1/2cupfinely chopped green pepper
1to 3 hot chilesanywhere from Tabasco to jalapeno, finely chopped
1to 2 tablespoons Cajun seasoning
4green onions. chopped
Cook the rice as usual. Move the cooked rice to a sheet pan and lay it out to cool. You need to start with cool rice. And yes, you can do this step a day ahead if you want.
If you are using gizzards, clean them of grit and that silver membrane and either chop fine or grind in a meat grinder. A meat grinder is better, but not everyone has one. Alternately, you can use any ground meat. Either finely grind or finely chop the livers.
Heat the duck fat over medium-high heat and, when it is hot, add the ground gizzards and the chopped livers. Toss to coat in the fat and then let them sit a bit to develop a crust on the bottom of the pan. Stir only occasionally, as you want to develop a good crust. If your Cajun seasoning isn't salty, salt the meat now.
Pour about 1/4 cup of the broth into the pan and use it to scrape up the browned bits on the bottom of the pan. Add the onion, peppers, celery and garlic. Mix to combine and Cook for a solid 3 to 5 minutes, until the vegetables are soft.
Sprinkle over the oregano and the Cajun seasoning and let a crust form on the bottom of the pan again. When it does, add the rest of the broth and the rice and mix to combine. Scrape the bottom of the pan again. When the liquid has almost totally evaporated, mix in the green onions. You're ready when the liquid has all evaporated. Serve hot.
Serve this on its own for a light dinner, or as a side dish to gumbo, or roast birds or venison.