First, make the roux by placing the flour and 4 tablespoons of the butter into a small skillet over medium heat and whisk together.
Continue to whisk until the mixture turns medium to dark brown, about 5 minutes. Set aside off the heat.
Place a Dutch oven or thick-bottomed large skillet over medium heat. Melt the remaining butter.
Add the kielbasa, cumin, pepper, and paprika.
Brown the sausage, fixing it with the spices and letting it brown. Bits will stick to the bottom of the pan.
Deglaze the pan with ½ cup of the stock, scraping off all the browned bits on the bottom of the pan.
Add the garlic and mix in until fragrant, about 1 minute.
Add the roux and stir until well combined.
Cook uncovered for 10 minutes, adding the remaining stock slowly so the mixture doesn’t completely dry out. Stir occasionally. If it seems too juicy, continue cooking until most of the liquid is absorbed.
Add the rice and green onions, stir to combine everything, and serve.