Heat the olive oil in a large pot or skillet over medium heat. Add the smoked sausage rounds in a single layer and sprinkle them with salt and pepper. Brown on one side, then flip the rounds and brown on the other side. When they are all brown, transfer to a plate.
In the same skillet, add the peppers, shallot and garlic. Sprinkle in more salt and pepper. Cook, stirring often, for 5 to 6 minutes or until the vegetables soften.
Add the rice into the skillet. Stir and cook for 2 to 3 minutes, allowing the rice to toast slightly.
Add the sausage back into the pot. Add 3 cups of the chicken stock. Bring the mixture to a boil. Reduce it to a simmer and cover. Cook for 10 minutes, then check to see if the liquid is absorbed. If the rice seems too dry, you can always add in a bit more liquid ½ cup at a time. The jasmine rice usually cooks quickly - within 10 to 20 minutes. If you use another kind of rice, you might need to add more liquid and cook it longer.
Once the rice is finished, sprinkle on some green onions. Serve and enjoy!