Combine the rice, 4 cups water and 1 tablespoon of salt in a large saucepan, cover and bring to a boil over high heat and cook until the grains open all the way, about 1 1/4 to 1 1/2 hours. The rice should be very cooked (not even the slightest chewy). Drain well, place in a large bowl and set aside.
Preheat the oven to 375 degrees F. Butter a 13x9x2 -inch baking dish.
Heat 1 tablespoon of the butter in a medium saute pan over high heat. Add the chorizo and cook until golden brown. Remove the sausage with a slotted spoon to a plate lined with paper towels.
Melt the remaining butter in a large saute pan over medium-high heat. Add the onions, carrots and celery and cook until soft, 4 to 5 minutes. Add the garlic and thyme and cook for 1 minute.
Add the onion mixture, bread, parsley, 3 cups of the chicken stock and the egg to the rice and mix well to combine. The mixture should be very wet; add more stock, if needed. Fold in the goat cheese and season with salt and pepper to taste.
Transfer the mixture to the prepared baking dish and bake, uncovered, until heated through and golden brown, about 30 minutes. Remove the dressing from the oven and let rest 10 minutes before serving.